The Dynamics of Comparative Advantage∗

Gordon H. Hanson†

UC San Diego and NBER

Nelson Lind§

UC San Diego

Marc-Andreas Muendler¶

UC San Diego and NBER

June 20, 2014

Abstract

We characterize the evolution of country export performance over the last five decades. Using the gravitymodel of trade, we extract a measure of country export capability by industry which we use to evaluatehow absolute advantage changes over time for 135 industries in 90 countries. We alternatively use theBalassa RCA index as a measure of comparative advantage. Part I of the analysis documents two em-pirical regularities in country export behavior. One is hyperspecialization: in the typical country, exportsuccess is concentrated in a handful of industries. Hyperspecialization is consistent with a heavy uppertail in the distribution of absolute advantage across industries within a country, which is well approxi-mated by a generalized gamma distribution whose shape is stable both across countries and over time.The second empirical regularity is a high rate of turnover in a country’s top export industries. Churningin top exports reflects mean reversion in a typical country’s absolute advantage, which we estimate tobe on the order of 30% per decade. Part II of the analysis reconciles hyperspecialization in exports withhigh decay rates in export capability by modeling absolute advantage as a stochastic process. We specifya generalized logistic diffusion for absolute advantage that allows for Brownian innovations (accountingfor surges in a country’s export prowess), a country-wide stochastic trend (flexibly transforming absoluteinto comparative advantage), and deterministic mean reversion (permitting export surges to be imperma-nent). To gauge the fit of the model, we take the parameters estimated from the pooled time series andproject the cross-sectional distribution of absolute advantage for each country in each year. Based onjust three global parameters, the simulated values match the cross-sectional distributions—which are nottargeted in the estimation—with considerable accuracy. Our results provide an empirical road map fordynamic theoretical models of the determinants of comparative advantage.

∗Ina Jäkle and Heea Jung provided excellent research assistance. We thank Dave Donaldson, Davin Chor, Sam Kortum and BenMoll as well as seminar participants at NBER ITI, Carnegie Mellon U, UC Berkeley, Brown U, U Dauphine Paris, the West CoastTrade Workshop UCLA, CESifo Munich, and the Cowles Foundation Yale for helpful discussions and comments.

†IR/PS 0519, University of California, San Diego, 9500 Gilman Dr, La Jolla, CA 92093-0519 (gohanson@ucsd.edu)§econweb.ucsd.edu/ nrlind, Dept. of Economics, University of California, San Diego, 9500 Gilman Dr MC 0508, La Jolla, CA

92093-0508 (nrlind@ucsd.com).¶www.econ.ucsd.edu/muendler, Dept. of Economics, University of California, San Diego, 9500 Gilman Dr MC 0508, La Jolla,

CA 92093-0508 (muendler@ucsd.edu). Further affiliations: CAGE and CESifo.

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1 Introduction

Comparative advantage has made a comeback in international trade. After a long hiatus during which the

Ricardian model was universally taught to undergraduates but rarely used in quantitative research, the role of

comparative advantage in explaining trade flows is again at the center of inquiry. Its resurgence is due in part

to the success of the Eaton and Kortum (2002) model (EK hereafter), which gives a probabilistic structure

to firm productivity and allows for settings with many countries and many goods.1 On the empirical side,

Costinot et al. (2012) uncover strong support for a multi-sector version of EK in cross-section data for

OECD countries. Another source of renewed interest in comparative advantage comes from the dramatic

recent growth in North-South and South-South trade (Hanson 2012). The emerging-economy examples

of China and Mexico specializing in labor-intensive manufactures, Brazil and Indonesia concentrating in

agricultural commodities, and Peru and South Africa shipping out large quantities of minerals give the

strong impression that resource and technology differences between countries have a prominent role in

determining current global trade flows.

In this paper, we characterize the evolution of country export advantages over the last five decades. Using

the gravity model of trade, we extract a measure of country export capability which we use to evaluate how

export performance changes over time for 135 industries in 90 countries between 1962 and 2007. Distinct

from Costinot et al. (2012) and Levchenko and Zhang (2013), our gravity-based approach does not use

industry production or price data to evaluate countries’ export prowess. Instead, we rely on trade data only,

which allows us to impose less theoretical structure on the determinants of trade, examine industries at a fine

degree of disaggregation and over a long time span, and include both manufacturing and non-manufacturing

sectors in our analysis. These features help in identifying the stable and heretofore underappreciated patterns

of export dynamics that we uncover.

The gravity model is consistent with a large class of trade models (Anderson 1979, Anderson and van

Wincoop 2003, Arkolakis et al. 2012). These have in common an equilibrium relationship in which bilat-

eral trade in a particular industry and year can be decomposed into three components (Anderson 2011): an

exporter-industry fixed effect, which captures the exporting country’s average export capability in an indus-

try; an importer-industry fixed effect, which captures the importing country’s effective demand for foreign

goods in an industry; and anexporter-importer component, which captures bilateral trade costs between

pairs of exporting and importing countries. We estimate these components for each year in our data, with

and without correcting for zero trade flows.2 In the EK model, the exporter-industry fixed effect is the prod-

1Shikher (2011, 2012) expand EK to a multi-industry setting.2See Silva and Tenreyro (2006), Helpman et al. (2008), Eaton et al. (2012), and Fally (2012) for alternative econometric

approaches to account for zero trade between countries.

2

uct of a country’s overall efficiency in producing goods and its unit production costs. In the Krugman (1980),

Heckscher-Ohlin (Deardorff 1998), Melitz (2003), and Anderson and van Wincoop (2003) models, which

also yield gravity specifications, the form of the exporter-industry component differs but its interpretation as

a country-industry’s export capability still applies. By taking the deviation of a country’s export capability

from the global mean for the industry, we obtain a measure of a country’s absolute advantage in an industry.

This definition is equivalent to a country’s share of world exports in an industry that we would obtain were

trade barriers in importing countries non-discriminating across exporters. By further normalizing absolute

advantage by a country-wide term, we remove the effects of aggregate country growth, focusing attention

on how the ranking of a country’s export performance across industries changes over time. We refer to

export capability after its double normalization by global-industry and country-wide terms as a measure of

comparative advantage.

The aim of our analysis is to identify the dynamic empirical properties of absolute and comparative ad-

vantage that any theory of their determinants must explain. Though we motivate our approach using EK, we

remain agnostic about the origins of a country’s export strength. Export capability may depend on the accu-

mulation of ideas (Eaton and Kortum 1999), home-market effects (Krugman 1980), relative factor supplies

(Trefler 1995, Davis and Weinstein 2001, Romalis 2004, Bombardini et al. 2012), the interaction of industry

characteristics and country institutions (Levchenko 2007, Costinot 2009, Cuñat and Melitz 2012), or some

combination of these elements. Rather than search for cross-section covariates of export capability, as in

Chor (2010), we seek the features of its distribution across countries, industries, and time. For robustness,

we repeat the analysis by replacing our gravity-based measure of export capability with Balassa’s (1965)

index of revealed comparative advantage (RCA) and obtain similar results. We further restrict the period

to 1984 and later, when more detailed industry data are available. This more recent period allows us to

vary industry aggregation from two-digit to four-digit sectors, and we demonstrate that our results are not a

byproduct of sector definitions.

After estimating country-industry export capabilities, our analysis proceeds in two stages. First, we

document two strong empirical regularities in country export behavior that are seemingly in opposition to

one another but whose synthesis reveals stable underlying patterns in the evolution of export advantage. One

regularity is hyperspecialization in exporting.3 In any given year, exports in the typical country tend to be

highly concentrated in a small number of industries. Across the 90 countries in our data, the median share

for the single top good (out of 135) in a country’s total exports is 21%, for the top 3 goods is 45%, and for

the top 7 goods is 64%. Consistent with strong concentration, the cross-industry distribution of absolute

3See Easterly and Reshef (2010), Hanson (2012), and Freund and Pierola (2013) for related findings.

3

advantage for a country in a given year is heavy tailed and approximately log normal, with ratios of the

mean to the median of about 7. Strikingly, this approximation applies to countries specializing in distinct

types of goods and at diverse stages of economic development. The Balassa RCA index is similarly heavy

tailed.

Stability in the shape of the distribution of absolute advantage makes the second empirical regular-

ity regarding exports all the more surprising: there is steady turnover in a country’s top export products.

Among the goods that account for the top 5% of a country’s absolute-advantage industries in a given year,

nearly 60% were not in the top 5% two decades earlier. Such churning is consistent with mean reversion in

export superiority, which we confirm by regressing the change in a country-industry’s absolute advantage

on its initial value, obtaining decadal decay rates on the order of 25% to 30%. These regressions control

for country-time fixed effects, and so may be interpreted as summarizing the dissipation of comparative

advantage. The mutability of a country’s relative export capabilities is consistent with Bhagwati’s (1994)

description of comparative advantage as “kaleidoscopic,” with the dominance of a country’s top export

products often being short lived.

A concern about log normality in absolute advantage is whether it may be a byproduct of the estimation

of the exporter-industry fixed effects. If these fixed effects varied randomly around a common mean for

a country, they would be approximately normally distributed around a constant expected value, making

absolute advantage tend toward log normality. Such logic, however, rests on the exporter-industry fixed

effects having a common country mean. Our central focus is precisely on how mean export capability varies

across industries for a country and how this variation progresses over time. Incidental log normality—

resulting, say, from classical measurement error in trade data—would imply that in our decay regressions

mean reversion in log absolute advantage from one period to the next would be more or less complete. Yet,

this is not what we find. Mean reversion is partial, with estimated annual decay rates being similar whether

based on 5, 10, or 20-year changes. Moreover, subsequent shocks to absolute advantage preserve the shape

of its cross sectional distribution within a country. This subtle balance between mean reversion and random

innovation, which also holds for the RCA index, is highly suggestive of a stochastic growth process at work

for individual industries.

In the second stage of our analysis, we seek to characterize the stochastic process that guides export

capability and thereby reconcile hyperspecialization in exports with mean reversion in export advantage.

We specify a generalized logistic diffusion for absolute advantage that allows for Brownian innovations

(accounting for surges in a country’s relative export prowess), a country-wide stochastic trend (flexibly

transforming absolute into comparative advantage), and deterministic mean reversion (permitting export

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surges to be impermanent). The generalized logistic diffusion that we specify has the generalized gamma as

a stationary distribution.4 The generalized gamma unifies the gamma and extreme-value families (Crooks

2010) and therefore flexibly nests many common distributions. To gauge the fit of the model, we take

the three global parameters estimated from the pooled countrytime seriesand project thecross-section

distribution of absolute advantage, which is not targeted in the estimation, for each country in each year.

Based on just these three parameters (and controlling for a country-wide stochastic trend), the simulated

values match the cross-sectional distributions, country-by-country and period-by-period, with considerable

accuracy. The stochastic nature of absolute advantage implies that, at any moment in time, a country is

especially strong at exporting in only a few industries and that, over time, this strength is temporary, with

the identity of top industries churning perpetually.

We then allow model parameters to vary by groups of countries and by broad industry and estimate them

for varying levels of industry aggregation. The three parameters of the generalized gamma govern the rate

at which the process reverts to the global long-run mean (the dissipation of comparative advantage), the

degree of asymmetry in mean reversion from above versus below the mean (the stickiness of comparative

advantage), and the rate at which industries are reshuffled within the distribution (the intensity of innovations

in comparative advantage). The first two parameters alone determine the shape of the stationary cross

sectional distribution, with the third determining how quickly convergence to the long-run distribution is

achieved. The intensity of innovations is stronger for developing than for developed economies. Whereas

comparative advantage dissipates more quickly for manufacturing than for non-manufacturing industries, it

is also relatively sticky for manufacturing, implying that industries revert towards the long-term mean more

slowly from a position of comparative advantage than from a position of disadvantage.

A growing literature, to which our work contributes, employs the gravity model of trade to estimate the

determinants of comparative advantage.5 In exercises based on cross-section data, Chor (2010) explores

whether the interaction of industry factor intensity with national characteristics can explain cross-industry

variation in export volume and Waugh (2010) identifies asymmetries in trade costs between rich and poor

countries that contribute to cross-country differences in income. In exercises using data for multiple years,

Fadinger and Fleiss (2011) find that the implied gap in countries’ export capabilities vis-a-vis the United

States closes as countries’ per capita GDP converges to U.S. levels,6 and Levchenko and Zhang (2013), who

calibrate the EK model to estimate overall sectoral efficiency levels by country, find that these efficiency

4Kotz et al. (1994) present properties of the generalized gamma distribution. Cabral and Mata (2003) use the generalized gammadistribution to study firm-size distributions. The finance literature considers a wide family of stochastic asset price processes withlinear drift and power diffusion terms (see, e.g., Chan et al. 1992, on interest rate movements). Those specifications nest neither anordinary nor a generalized logistic diffusion.

5On changes in export diversification over time see see Imbs and Wacziarg (2003) and Cadot et al. (2011).6Related work on gravity and industry-level productivity includes Finicelli et al. (2009, 2013) and Kerr (2013).

5

levels converge across countries over time, weakening comparative advantage in the process.7

Our approach differs from the literature in two notable respects. By not using functional forms specific

to EK or other trade models, we free ourselves from having to use industry production data (which is

necessary to pin down model parameters) and are thus able to examine all merchandise sectors, including

non-manufacturing, at the finest level of industry disaggregation possible. We gain from this approach a

perspective on hyperspecialization in exporting and churning in top export goods that is less apparent in data

limited to manufacturing or based on more aggregate industry categories. We lose, however, the ability to

evaluate the welfare consequence of changes in comparative advantage (as in Levchenko and Zhang 2013).

A second distinctive feature of our approach is that we treat export capability as being inherently dynamic.

Previous work tends to study comparative advantage by comparing repeated static outcomes over time. We

turn the empirical approach around, and estimate the underlying stochastic process itself. The virtue is that

we can then predict the distribution of export advantage in the cross section, which our estimator does not

target, and use the the cross-section projections as a check on the goodness of fit.

Section 2 of the paper presents a theoretical motivation for our gravity specification. Section 3 describes

the data and our estimates of country export capabilities, and documents empirical regularities regarding

comparative advantage, hyperspecialization in exporting and churning in countries’ top export goods. Sec-

tion 4 describes a stochastic process that has a cross sectional distribution consistent with hyperspecial-

ization and a drift consistent with turnover, and introduces a GMM estimator to identify the fundamental

parameters. Section 5 presents the estimates and evaluates the fit of the diffusion. Section 6 concludes.

2 Theoretical Motivation

In this section, we use the EK model to motivate our definitions of export capability and absolute advantage

and then describe our approach for extracting these values from the gravity model of trade.

2.1 Export capability and comparative advantage

In the EK model, an industry consists of many product varieties. The productivityq of a source countrys

firm that manufactures a variety in industryi is determined by a random draw from a Fréchet distribution

with CDF FQ(q) = exp{−(q/qis)−θi} for q > 0. Consumers, who have CES preferences over product

varieties within an industry, buy from the firm that is able to deliver a variety at the lowest price. With firms

7Other related literature includes dynamic empirical analyses of the Heckscher-Ohlin model that examine how trade flowschange in response to changes in country factor supplies (Schott 2003, Romalis 2004) and work by Hausmann et al. (2007) on howthe composition of exports relates to the pace of economic growth.

6

pricing according to marginal cost, a higher productivity draw makes a firm more likely to be the low-priced

supplier of a variety to a given market.

Comparative advantage stems from the position of the industry productivity distribution, given byqis

.

The position can differ across source countriess and industriesi. In countries with a higherqis

, firms

are more likely to have a higher productivity draw, creating cross-country variation in the fraction of firms

that succeed within an industry in being low-cost suppliers to different destination markets.8 Consider the

many-industry version of the EK model in Costinot et al. (2012). Exports by source countrys to destination

countryd in industryi can be written as,

Xisd =

(

wsτisd/qis

)−θi

∑

s′

(

ws′τis′d/qis′

)−θiµiYd, (1)

wherews is the unit production cost for countrys, τisd is the iceberg trade cost betweens andd in industry

i, µi is the Cobb-Douglas share of expenditure on industryi, andYd is total expenditure in countryd. Taking

logs of (1), we obtain a gravity equation for bilateral trade

lnXisd = kis +mid − θi ln τisd, (2)

wherekis ≡ θ ln(qis/ws) is source countrys’s log export capabilityin industryi, which is a function of the

country’s overall efficiency in the industry (qis

) and its unit production costs (ws), and

mid ≡ ln

[

µiYd/∑

s′

(

ws′dis′d/qis′

)−θi]

is the log ofeffective import demandby countryd in industryi, which depends on the country’s expenditure

on goods in the industry divided by an index of the toughness of competition for the country in the industry.

Export capability is a function of a primitive country characteristic—the position of a country’s produc-

tivity distribution—and of endogenously determined unit production costs. EK does not yield a closed-form

solution for wages, we can therefore not solve for export capabilities as explicit functions of theqis

’s. Yet,

in a model with a single factor of production theqis

’s are the only country-specific variable for the in-

dustry (other than population and trade costs) that may determine factor prices, meaning that thews’s are

implicit functions of these parameters. Our concept of export capabilitykis can further be related to the

8The importance of the position of the productivity distribution for trade depends in turn on the shape of the distribution, givenby θi. Lower dispersion in productivity draws (a higher value ofθi) elevates the role of the distribution’s position in determininga country’s strength in an industry. These two features—the country-industry position parameterq

isand the industry dispersion

parameterθi—pin down a country’s export capability.

7

deeper origins of comparative advantage by modeling the country-industry-specific Fréchet position param-

eterTis ≡ (qis)θi as the outcome of an exploration and innovation process, similar to Eaton and Kortum

(1999), a connection we sketch in Appendix D.

Any trade model that has a gravity structure will generate exporter-industry fixed effects and a reduced-

form expression for exporter capability. In the Armington (1969) model, as applied by Anderson and van

Wincoop (2003), export capability is a country’s endowment of a good relative to its remoteness from the

rest of the world. In Krugman (1980), export capability equals the number of varieties a country produces

in an industry times effective industry marginal production costs. In Melitz (2003), export capability is

analogous to that in Krugman adjusted by the Pareto lower bound for productivity in the industry, with the

added difference that bilateral trade is a function of both variable and fixed trade costs. And in a Heckscher-

Ohlin model (Deardorff 1998), export capability reflects the relative size of a country’s industry based

on factor endowments and sectoral factor intensities. The common feature of these models is that export

capability is related to a country’s productive potential in an industry, be it associated with resource supplies,

a home-market effect, or the distribution of firm-level productivity.

The principle of comparative advantage requires that a country-industry’s export capabilityKis ≡

exp{kis} be compared to both the same industry across countries and to other industries within the same

country. This double comparison of a country-industry’s export capability to other countries and other

industries is also at the core of measures of revealed comparative advantage (Balassa 1965) and recent im-

plementations of comparative advantage, as in Costinot et al. (2012). Consider two exporterss ands′ and

two industriesi andi′, and define geography-adjusted trade flows as

Xisd ≡ Xisd (τisd)θi =

(

ws/qis

)−θiexp{mid}.

The correction of observed tradeXisd by trade costs(τisd)θ removes the distortion that geography exerts

on export capability when trade flows are realized.9 When compared to any countrys′, countrys has a

comparative advantage in industryi relative to industryi′ if the following condition holds:

Xisd/Xis′d

Xi′sd/Xi′s′d

=Kis/Kis′

Ki′s/Ki′s′> 1. (3)

The comparison of a country-industry to the same industry in other source countries makes the measure

independent of destination-market characteristicsmid because the standardizationXisd/Xis′d removes the

destination-market term. In practice, a large number of industries and countries makes it cumbersome to

9This adjustment ignores any impact of trade costs on equilibrium factor pricesws.

8

conduct double comparisons of a country-industryis to all other industries and all other countries. Our

gravity-based correction of trade flows for geographic frictions gives rise to a natural alternative summary

measure.

2.2 Estimating the gravity model

By allowing for measurement error in trade data or unobserved trade costs, we introduce a disturbance term

into (2), converting it into a regression model. With data on bilateral industry trade flows for many importers

and exporters, we can obtain estimates of the exporter-industry and importer-industry fixed effects via OLS.

The gravity model that we estimate is

lnXisdt = kist +midt − bitDsdt + ǫisdt, (4)

where we have added a time subscriptt, we include dummy variables to measure exporter-industry-yearkist

and importer-industry-yearmidt terms,Dsdt represents the determinants of bilateral trade costs, andǫisdt

is a residual that is mean independent ofDsdt. The variables we use to measure trade costsDsdt in (4) are

standard gravity covariates, which do not vary by industry.10 However, we do allow the coefficientsbit on

these variables to differ by industry and by year.11 Absent annual measures of industry-specific trade costs

for the full sample period, we model these costs via the interaction of country-level gravity variables and

time-and-industry-varying coefficients.

In the estimation, we exclude a constant term, include an exporter-industry-year dummy for every ex-

porting country in each industry, and include an importer-industry-year dummy for every importing country

except for one, which we select to be the United States. The exporter-industry-year dummies we estimate

thus equal

kOLSist = kist +miUS t, (5)

wherekOLSist is the estimated exporter-industry dummy for countrys in industryi and yeart, miUS t is the

U.S. importer-industry-year fixed effect, andkist is the underlying log export capability. The estimator of

the exporter-industry variables is therefore meaningful only up to an industry normalization.

The values that we will use for empirical analysis are the deviations of the estimated exporter-industry-

10These include log distance between the importer and exporter, the time difference (and time difference squared) between theimporter and exporter, a contiguity dummy, a regional trade agreement dummy, a dummy for both countries being members ofGATT, a common official language dummy, a common prevalent language dummy, a colonial relationship dummy, a commonempire dummy, a common legal origin dummy, and a common currency dummy.

11We estimate (4) separately by industry and by year. Since the regressors are the same across industries for each bilateral pair,there is no gain to pooling data across industries in the estimation, which helps reduce the number of parameters to be estimated ineach regression.

9

year dummies from the global industry means:

kist = kOLSist −

1

S

N∑

s′=1

kOLSis′t , (6)

where the deviation removes the excluded importer-industry-year term as well as any global industry-

specific term. This normalization obviates the need to account for worldwide industry TFP growth, demand

changes, or producer price index movements, allowing us to conduct analysis of comparative advantage with

trade data exclusively.

From this exercise, we take as a measure ofabsolute advantageof countrys’s industryi,

Aist ≡ exp{kist} =exp {kOLS

ist }

exp{

1S

∑Ss′=1 k

OLSis′t

} =exp {kist}

exp{

1S

∑Ss′=1 kis′t

} . (7)

By construction, this measure is unaffected by the choice of the omitted importer-industry-year fixed effect.

As the final equality in (7) shows, the measure is equivalent to the comparison of underlying exporter

capabilityKist to the geometric mean of exporter capability across countries in industryi.

There is some looseness in our measure of absolute advantage. WhenAist rises for country-industryis,

we say that its absolute advantage has risen even though it is only strictly true that its export capability has

increased relative to the global industry geometric mean. In truth, the country’s export capability may have

risen relative to some countries and fallen relative to others. Our motivation for using the deviation from the

geometric mean to define absolute advantage is twofold. One is that our statistic removes the global industry

component of estimated export capability, making our measure immune to the choice of normalization in

the gravity estimation. Two is that removing the industry-year component relates naturally to specifying a

stochastic process for export capability. Rather than modeling export capability itself, we model its devia-

tion from an industry trend, which simplifies the estimation by freeing us from having to model the trend

component that will reflect global industry demand and supply. We establish the main regularities regarding

the cross section and the dynamics of exporter performance using absolute advantageAist in Section 3. In

Section 4, we let the stochastic process that is consistent with the empirical regularities of absolute advan-

tage determine the remaining country-level standardization that transforms absolute advantageAist into a

measure of comparative advantage.

As is well known, the gravity model in (2) and (4) is inconsistent with the presence of zero trade flows,

which are common in bilateral data. We recast EK to allow for zero trade by following the approach in Eaton

et al. (2012), who posit that in each industry in each country only a finite number of firms make productivity

10

draws, meaning that in any realization of the data there may be no firms from countrys that have sufficiently

high productivity to profitably supply destination marketd in industryi. In their framework, the analogue

to equation (1) is an expression for the expected share of countrys in the market for industryi in countryd,

E [Xisd/Xid], which can be written as a multinomial logit. This approach, however, requires that one know

total expenditure in the destination market,Xid, including a country’s spending on its own goods. Since

total expenditure is unobserved in our data, we apply the independence of irrelevant alternatives and specify

the dependent variable as the expectation for an exporting country’s share of total import purchases in the

destination market:

E

[

Xisd∑

s′ 6=dXis′d

]

=exp (kist − bitDisdt)

∑

s′ 6=d exp (kis′t − bitDis′dt). (8)

We re-estimate exporter-industry-year fixed effects by applying multinomial pseudo-maximum likelihood

to (8).12

Our baseline measure of absolute advantage relies on regression-based estimates of exporter-industry-

year fixed effects. Even when following the approach in Eaton et al. (2012), estimates of these fixed effects

may become imprecise when a country exports a good to only a few destinations. As an alternative measure

of export performance, we use the Balassa (1965) measure of revealed comparative advantage, defined as,

RCAist =

∑

dXisdt/∑

i′∑

d′ Xi′s′d′t∑

i′∑

dXi′sdt/∑

s′∑

i′∑

d′ Xi′s′d′t(9)

While the RCA index is ad hoc and does not correct for distortions in trade flows introduced by trade

costs or proximity to market demand, it has the appealing attribute of being based solely on raw trade data.

Throughout our analysis we will employ the gravity-based measure of absolute advantage alongside the

Balassa RCA measure. Reassuringly, our results for the two measures are quite similar.

3 Data and Main Regularities

The data for our analysis are World Trade Flows from Feenstra et al. (2005),13 which are based on SITC

revision 1 industries for 1962 to 1983 and SITC revision 2 industries for 1984 and later.14 We create a

consistent set of country aggregates in these data by maintaining as single units countries that divide over

the sample period.15 To further maintain consistency in the countries present, we restrict the sample to

12We thank Sebastian Sotelo for estimation code.13We use a version of these data that have been extended to 2007 by Robert Feenstra and Gregory Wright.14A further source of observed zero trade is that for 1984 and later bilateral industry trade flows are truncated below $100,000.15These are the Czech Republic, the Russian Federation, and Yugoslavia. We also join East and West Germany, Belgium and

Luxembourg, and North and South Yemen.

11

nations that trade in all years and that exceed a minimal size threshold, which leaves 116 country units.16

The switch from SITC revision 1 to revision 2 in 1984 led to the creation of many new industry categories.

To maintain a consistent set of SITC industries over the sample period, we aggregate industries from the

four-digit to three-digit level.17 These aggregations and restrictions leave 135 industries in the data. In an

extension of our main results, we limit the sample to SITC revision 2 data for 1984 forward, alternatively

using two-digit (61 industries), three-digit (227 industries), or four-digit (684 industries) sector definitions.

A further set of country restrictions are required to estimate importer and exporter fixed effects. For

coefficients on exporter-industry dummies to be comparable over time, the countries that import a good

must do so in all years. Imposing this restriction limits the sample to 46 importers, which account for an

average of 92.5% of trade among the 116 country units. We also need that exporters ship to overlapping

groups of importing countries. As Abowd et al. (2002) show, such connectedness assures that all exporter

fixed effects are separately identified from importer fixed effects.18 This restriction leaves 90 exporters in the

sample that account for an average of 99.4% of trade among the 116 country units. Using our sample of 90

exporters, 46 importers, and 135 industries, we estimate the gravity equation (4) separately by industryi and

yeart and then extract absolute advantageAist given by (7). Data on gravity variables are from CEPII.org.

3.1 Hyperspecialization in exporting

We first characterize export behavior in the cross section of industries for each country at a given moment

of time. For an initial take on the concentration of exports in leading products, we tabulate the share of

a country-industry’s exportsXist/(∑

i′ Xi′st) in the country’s total exports across the 135 industries. We

then average these shares across the current and preceding two years to account for measurement error and

cyclical fluctuations. InFigure 1a, we display median export shares across the 90 countries in our sample

for the top export industry as well as the top three, top seven, and top 14 industries, which roughly translate

into the top 1%, 3%, 5% and 10% of products.

For the typical country, a handful of industries dominate exports.19 The median export share of just16This reporting restriction leaves 141 importers (97.7% of world trade) and 139 exporters (98.2% of world trade) and is roughly

equivalent to dropping small countries from the sample. For consistency in terms of country size, we drop countries with fewer than1 million inhabitants in 1985 (42 countries had 1985 population less than 250,000, 14 had 250,000 to 500,000, and 9 had 500,000to 1 million), which reduces the sample to 116 countries (97.4% of world trade).

17There are 226 three-digit SITC industries that appear in all years, which account for 97.6% of trade in 1962 and 93.7% in 2007.Some three-digit industries frequently have their trade reported only at the two-digit level (which accounts for the just reporteddecline in trade shares for three-digit industries). We aggregate over these industries, creating 143 industry categories that are amix of SITC two and three-digit products. From this group we drop nonstandard industries (postal packages, coins, gold bars, DCcurrent) and three industries that are always reported as one-digit aggregates in the US data. We further exclude oil and natural gas,which in some years have estimated exporter-industry fixed effects that are erratic.

18Countries that export to mutually exclusive sets of destinations would not allow us to separately identify the exporter fixedeffect from the importer fixed effects.

19In analyses of developing-country trade, Easterly and Reshef (2010) document the tendency of a small number of bilateral-

12

Figure 1:Concentration of Exports

(1a) All exporters (1b) LDC exporters

.1.2

.3.4

.5.6

.7.8

.9S

hare

of t

otal

exp

orts

1967 1972 1977 1982 1987 1992 1997 2002 2007

Median share of exports in top goods, all exporters

Top good (1%) Top 3 goods (2%)Top 7 goods (5%) Top 14 goods (10%)

.1.2

.3.4

.5.6

.7.8

.9S

hare

of t

otal

exp

orts

1967 1972 1977 1982 1987 1992 1997 2002 2007

Median share of exports in top goods, LDC exporters

Top good (1%) Top 3 goods (2%)Top 7 goods (5%) Top 14 goods (10%)

Source:WTF (Feenstra et al. 2005, updated through 2008) for 135 time-consistent industries in 90 countries from 1962-2007.Note: Shares of industryi’s export value in countrys’s total export value:Xist/(

∑i′ Xi′st). For the classification of less developed

countries (LDC) see Appendix E.

the top export good is 24% in 1972, which declines modestly over time to 20% by 2007. Over the full

period, the median export share of the top good averages 21%. For the top three products, the median

export share declines slightly from the 1960s to the 1970s and then is stable from the early 1980s onward

at approximately 42%. The median export shares of the top seven and top 14 products display a similar

pattern, stabilizing by the early 1980s at around 62% and 77%, respectively. Thus, the bulk of a country’s

exports tend to be accounted for by the top 10% of its goods. InFigure 1b, we repeat the exercise, limiting

the sample to less developed countries (see Appendix E). The patterns are quite similar to those for all

countries, though median export shares for LDCs are modestly higher in the reported quantiles.

One concern about using export shares to measure export concentration is that these values may be

distorted by demand conditions. Exports in some industries may be large simply because these industries

capture a relatively large share of global expenditure, leading the same industries to be top export industries

in all countries. In 2007, for instance, the top export industry in Great Britain, France, Germany, Japan,

and Mexico is road vehicles. In the same year in Korea, Malaysia, the Philippines, Taiwan, and the United

States the top industry is electric machinery. One would not want to conclude from this fact that each of

these countries has an advantage in exporting one of these two products.

To control for variation in industry size that is associated with preferences, we turn to our measure of

industry relationships to dominate national exports and Freund and Pierola (2013) describe the prominent role of the largest fewfirms in countries’ total foreign shipments.

13

absolute advantage in (7) expressed in logs aslnAist = kist. As this value is the log industry export capabil-

ity in a country minus global mean log industry export capability, industry characteristics that are common

across countries—including the state of global demand—are differenced out. To provide a sense of the iden-

tities of absolute-advantage goods and the magnitudes of their advantages, we show in AppendixTable A1

the top two products in terms ofAist for 28 of the 90 exporting countries, using 1987 and 2007 as represen-

tative years. To remove the effect of overall market size and thus make values comparable across countries,

we normalize log absolute advantage by its country mean, such that the value we report for country-industry

is is lnAist − (1/I)∑I

i′ lnAi′st. The country normalization yields a double log difference—a country’s

log deviation from the global industry mean minus its average log deviation across all industries—which is

a measure of comparative advantage.

There is considerable variation across countries in the top advantage industries. In 2007, comparative

advantage in Argentina is strongest in maize, in Brazil it is iron ore, in Canada it is wheat, in Germany it is

road vehicles, in Indonesia it is rubber, in Japan it is telecommunications equipment, in Poland it is furniture,

in Thailand it is rice, Turkey it is glassware, and in the United States it is other transport equipment (mainly

commercial aircraft). The implied magnitudes of these advantages are enormous. Among the 90 countries

in 2007, comparative advantage in the top product—i.e., the double log difference—is over 400 log points

in 76 of the cases. Further, the top industries in each country by and large correspond to those one associates

with national export advantages, suggesting that the observed rankings of export capability are not simply a

byproduct of measurement error in trade values.

To characterize the full distribution of absolute advantage across industries for a country, we next plot

the log number of a source countrys’s industries that have at least a given level of absolute advantage in a

yeart against that log absolute advantage levellnAist for industriesi. By design, the plot characterizes the

cumulative distribution of absolute advantage by country and by year (Axtell 2001, Luttmer 2007).Figure 2

shows the distribution plots of log absolute advantage for 12 countries in 2007. Plots for 28 countries in

1967, 1987 and 2007 are shown in AppendixFigures A1, A2 andA3. The figures also graph the fit of

absolute advantage to a Pareto distribution and to a log normal distribution using maximum likelihood,

where each distribution is fit separately for each country in each year (such that the number of parameters

estimated equals the number of parameters for a distribution× number of countries× number of years).

We choose the Pareto and the log normal as comparison cases because these are the standard options in the

literature on firm size (Sutton 1997). For the Pareto distribution, the cumulative distribution plot is linear in

the logs, whereas the log normal distribution generates a relationship that is concave to the origin. Relevant

to our later analysis, each is a special case of the generalized gamma distribution. To verify that the graphed

14

Figure 2:Cumulative Probability Distribution of Absolute Advantage for Select Countries in 2007

Brazil China Germany

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

India Indonesia Japan

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

Korea Rep. Mexico Philippines

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128N

umbe

r of

Indu

strie

s)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

Poland Turkey United States

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

Source:WTF (Feenstra et al. 2005, updated through 2008) for 135 time-consistent industries in 90 countries from 1962-2007 andCEPII.org; gravity-based measures of absolute advantage (7).Note: The graphs show the frequency of industries (the cumulative probability1 − FA(a) times the total number of industriesI = 135) on the vertical axis plotted against the level of absolute advantagea (such thatAist ≥ a) on the horizontal axis. Bothaxes have a log scale. The fitted Pareto and log normal distributions for absolute advantageAist are based on maximum likelihoodestimation by countrys in yeart = 2007.

15

cross-sectional distributions are not a byproduct of specification error in estimating export capabilities from

the gravity model, we repeat the plots using the Balassa (1965) RCA index, with similar results. And to

verify that the patterns we uncover are not a consequence of arbitrary industry aggregations we construct

plots at the two, three, and four-digit level based on SITC revision 2 data in 1987 and 2007, again with

similar results.20

The cumulative distribution plots clarify that the empirical distribution of absolute advantage is decid-

edly not Pareto. The log normal, in contrast, fits the data closely. The concavity of the cumulative distri-

bution plots drawn for the data indicate that gains in absolute advantage fall off progressively more rapidly

as one moves up the rank order of absolute advantage, a feature absent from the scale-invariant Pareto but

characteristic of the log normal. This concavity could indicate limits on industry export size associated with

resource depletion, congestion effects, or general diminishing returns. Though the log normal is a rough

approximation, there are noticeable discrepancies between the fitted log normal plots and the raw data plots.

For some countries, we see that compared to the log normal the number of industries in the upper tail drops

too fast (i.e., is more concave), relative to what the log normal distribution implies. These discrepancies

motivate our specification of a generalized logistic diffusion for absolute advantage in Section 4, which is

consistent with a generalized gamma distribution in the cross section.

Overall, we see that in any year countries have a strong export advantage in just a few industries, where

this pattern is stable both across countries and over time. Before examining the time series of comparative

advantage in more detail, we consider whether log normality in absolute advantage could be merely inci-

dental. The exporter-industry fixed effects are estimated mean values, which by the Central Limit Theorem

will converge to being normally distributed as the sample size becomes large. Incidental log normality in

absolute advantage could result if the estimated exporter-industry fixed effects varied randomly around a

common expected value for a given country. Our preferred view is that log normality in absolute advantage

results instead from differences in theindustry meansof export capability by country, where these indus-

try means determine comparative advantage. Indeed, if absolute advantage did have a common expected

value across industries for each country there would be no basis for comparative advantage at the industry

level. From the cross sectional distribution of absolute advantage alone, however, one cannot differentiate

between random variation in industry fixed effects around a common mean for each exporter and variation

in each exporter’s industry means. Examining how absolute advantage changes over time will help resolve

this issue.21

20Each of these additional sets of results is available in an online appendix.21It is worth noting that the hypothesis of incidental normality in the estimated exporter-industry fixed effects applies just as

readily to the estimated importer-industry fixed effects. As an instructive exercise, we also constructed cumulative distribution plots,analogous to those in AppendixFigures A1, A2andA3, for the estimated importer-industry fixed effects, which involves plotting

16

Figure 3:Absolute Advantage Transition Probabilities

(3a) All exporters (3b) LDC exporters

.1.2

.3.4

.5T

rans

ition

pro

babi

lity

1987 1992 1997 2002 2007

Position of products currently in top 5%, 20 years beforeExport transition probabilities (all exporters):

Above 95th percentile 85th−95th percentile60th−85th percentile Below 60th percentile

.1.2

.3.4

.5T

rans

ition

pro

babi

lity

1987 1992 1997 2002 2007

Position of products currently in top 5%, 20 years beforeExport transition probabilities (LDC exporters):

Above 95th percentile 85th−95th percentile60th−85th percentile Below 60th percentile

Source:WTF (Feenstra et al. 2005, updated through 2008) for 135 time-consistent industries in 90 countries from 1962-2007.Note: The graphs show the percentiles of productsis that are currently among the top 5% of products, 20 years earlier. The sample isrestricted to products (country-industries)is with current absolute advantageAist in the top five percentiles (1−FA(Aist) ≥ .05),and then grouped by frequencies of percentiles twenty years prior, where the past percentile is1 − FA(Ais,t−20) of the sameproduct (country-industry)is. For the classification of less developed countries (LDC) see Appendix E.

3.2 The dissipation of comparative advantage

The distribution plots of absolute advantage give an impression of stability. The strong concavity in the

plots is present in all countries and in all years. Yet, this stability masks considerable industry churning in

the distribution of absolute advantage, which we investigate next. Initial evidence of churning is evident in

AppendixTable A1. Between 1987 and 2007, Canada’s top good switches from sulfur to wheat, China’s

from explosives (fireworks) to telecommunications equipment, Egypt’s from cotton to crude fertilizers, In-

dia’s from tea to precious stones, Malaysia’s from rubber to radios, the Philippine’s from vegetable oils to

office machines, and Romania’s from furniture to footwear. Of the 90 total exporters, 70 exhibit a change in

the top comparative-advantage industry between 1987 and 2007. Moreover, most new top products in 2007

were not the number two product in 1987, but from lower down in the distribution. Churning thus appears

to be both pervasive and disruptive.

To characterize turnover in industry export advantage more completely, inFigure 3 we calculate the

fraction of top products in a given year that were also top products in previous years. We identify for each

country in each year where in the distribution the top 5% of absolute-advantage products (in terms ofAist)

exp {midt}, the exponentiated importer-industry fixed effect in equation (4), across industries for each country in representativeyears. The plots show little evidence of log normality for these values. In particular, the distribution of the exponentiated importer-industry fixed effects are much less concave to the origin than log normality would imply. These results are in the online appendix.

17

were 20 years before, with the options being top 5% of products, next 10%, next 25% or bottom 60%. We

then average across outcomes for the 90 exporters. The fraction of top 5% products in a given year that

were also top 5% products two decades before ranges from a high of 43% in 2002 to a low of 37% in 1997.

Averaging over all years, the share is 41%. There is thus nearly a 60% chance that a good in the top 5% in

terms of absolute advantage today was not in the top 5% two decades earlier. On average, 30% of new top

products come from the 85th to 95th percentiles, 16% come from the 60th to 85th percentiles, and 13% come

from the bottom six deciles. Figures are similar when we limit the sample to just developing economies.

Turnover in top export goods suggests that over time absolute advantage dissipates—countries’ strong

sectors weaken and some weak sectors strengthen. To evaluate this impermanence, we test for mean rever-

sion in log absolute advantage by estimating regressions of the form

lnAis,t+10 − lnAist = ρ lnAist + δst + εist. (10)

In (10), the dependent variable is the ten-year change in log absolute advantage and the predictors are the

initial value of log absolute advantage and dummy variables for the country-yearδst. Absolute advantage

represents the deviation in industry export capability for a country relative to the global mean. The inclusion

of country-year dummies introduces a further level of differencing from the country-year mean, so that the

regression in (10) evaluates the dynamics of comparative advantage. The coefficientρ captures the fraction

of comparative advantage that dissipates over the time interval of one decade, either decaying towards a log

level of zero when currently above or strengthening towards a log level of zero when currently below.

Table 1presents coefficient estimates for equation (10). The first two columns report results for all coun-

tries and industries, first for log absolute advantage in column 1 and next for the log RCA index in column 2.

Subsequent pairs of columns show results separately for less development countries and non-manufacturing

industries. Estimates forρ are uniformly negative and precisely estimated, consistent with mean reversion

in comparative advantage. For the sample of all industries and countries, estimates forρ in columns 1 and 2

are similar in value, equal to−0.24 when using log absolute advantage and−0.30 when using log RCA.

These magnitudes indicate that over the period of a decade the typical country-industry sees one-quarter

to three-tenths of its comparative advantage (or disadvantage) erode. In columns 3 and 4 we present com-

parable results for the subsample of developing countries. Decay rates appear to be larger for this group

of countries than worldwide average, indicating that in less developed economies mean reversion in com-

parative advantage is more rapid. In columns 5 and 6 we present results for only for non-manufacturing

industries, but all countries. For both measures of comparative advantage decay rates are larger in absolute

value for non-manufacturing industries (agriculture and mining), but the difference in decay rates between

18

Table 1: DECAY REGRESSIONS FORCOMPARATIVE ADVANTAGE

Full sample LDC exporters Non-manufacturingExp. cap.k RCA ln X Exp. cap.k RCA ln X Exp. cap.k RCA ln X

(1) (2) (3) (4) (5) (6)

Decay rateρ -0.237 -0.300 -0.338 -0.352 -0.359 -0.315(0.018)∗∗ (0.013)∗∗ (0.025)∗∗ (0.015)∗∗ (0.025)∗∗ (0.013)∗∗

Dissipation rateη 0.114 0.115 0.121 0.104 0.120 0.103(0.007)∗∗ (0.004)∗∗ (0.007)∗∗ (0.003)∗∗ (0.007)∗∗ (0.004)∗∗

Innov. intens.σ2 0.476 0.618 0.683 0.836 0.741 0.737(0.011)∗∗ (0.011)∗∗ (0.023)∗∗ (0.017)∗∗ (0.026)∗∗ (0.014)∗∗

Obs. 66,276 67,901 39,937 41,103 30,942 32,390Adj. R2 0.114 0.125 0.129 0.133 0.124 0.126

Source: WTF (Feenstra et al. 2005, updated through 2008) for 135 time-consistent industries in 90 countries from 1962-2007 andCEPII.org.Note: Reported figures for five-year decadalized changes. Variables are OLS-estimated gravity measures of export capabilitykby (5) and the log Balassa index of revealed comparative advantageln Xist = ln(Xist/

∑s′ Xis′t)/(

∑i′ Xi′st/

∑i′

∑s′ Xi′s′t).

OLS estimation of the decadal decay rateρ from

kis,t+10 − kist = ρ kist + δit + δst + εist,

conditional on industry-year and source country-year effectsδit andδst for the full pooled sample (column 1-2) and subsamples(columns 3-6). The implied dissipation rateη and innovation intensityσ2 are based on the decadal decay rate estimateρ andthe estimated variance of the decay regression residuals2 by (13). Less developed countries (LDC) as listed in Appendix E.Nonmanufacturing merchandise spans SITC sector codes 0-4. Standard errors (reported below coefficients) forρ are clustered bycountry and forη andσ are calculated using the delta method;∗∗ indicates significance at the 1% level.

non-manufacturing industries and the average industry is particularly pronounced for the log absolute ad-

vantage measure.22

As an additional robustness check on the decay regressions, we re-estimate (10) for the period 1984-

2007 using data from the SITC revision 2 sample. This allows us to perform regressions for log absolute

advantage and the log RCA index at the two, three and four-digit level. Results are reported in Appendix

Table A2. Estimated decay rates are comparable to those inTable 1. At the two-digit level (61 industries),

the decadal decay rate for absolute advantage using all countries and industries is 19%, at the three-digit

level (226 industries) it is 24%, and at the four-digit level (684 industries) it is 37%. When using the log

RCA index, decay rates vary less across aggregation levels, ranging from 26% at the two-digit level to 32%

at the four-digit level. The similarity in decay rates across definitions of comparative advantage and levels

of industry aggregation suggest that our results are neither merely generated by econometric estimation nor

the consequence of arbitrary industry definitions.

Our finding that decay rates imply less than complete mean reversion is evidence against the log normal-

ity of absolute advantage being incidental. Suppose the cumulative distribution plots inFigure 2 reflected

22In the next section, we offer further interpretation of these results.

19

random variation in log absolute advantage around a common expected value for each country in each year,

due say to measurement error in trade data. Under the assumption that this measurement error was classi-

cal, all within-country variation in the exporter-industry fixed effects would be the result of iid disturbances

that were uncorrelated across time. In the cross section, we would observe a log normal distribution for

absolute advantage—and possibly also for the RCA index—for each country in each year, with no temporal

connection between these distributions. When estimating the decay regression in (10), mean reversion in

absolute advantage would be complete, yielding a value ofρ equal or close to−1. The coefficient estimates

in Table 1 are strongly inconsistent with such a pattern. Instead, as we document next, the results reveal

that the stable cross sectional distribution of absolute absolute and the churn of industry export rankings are

intimately related phenomena.

3.3 Comparative advantage as a stochastic process

On its own, the finding that comparative advantage reverts to a long-term mean is uninformative about the

cross sectional distribution.23 While mean reversion is consistent with a stationary cross sectional distri-

bution, mean reversion is also consistent with a non-ergodic distribution and consistent with degenerate

comparative advantage that collapses at a long-term mean. Yet, the combination of mean reversion inTa-

ble 1 and temporal stability in the cumulative distribution plots inFigure 2 are strongly suggestive of a

balance between random innovations to export capability and the dissipation of these capabilities, a balance

characteristic of the class of stochastic processes that generate a stationary cross sectional distribution.

In exploring the dynamics of comparative advantage here and in Section (4) we limit ourselves to dif-

fusions: Markov processes for which all realizations of the random variable are continuous functions of

time and past realizations. As a preliminary exercise, we exploit the fact that the decay regression in (10)

is consistent with the discretized version of a commonly studied diffusion, the Ornstein-Uhlenbeck (OU)

process. Suppose that comparative advantage, which we express in continuous time asAis(t), follows an

OU process given by

d ln Ais(t) = −ησ2

2ln Ais(t) dt+ σ dWA

is (t) (11)

whereW Ais (t) is a Wiener process that induces stochastic changes in comparative advantage. The parameter

η regulates the rate of convergence at which comparative advantage reverts to its global long-run mean

and the parameterσ scales time and therefore the Brownian innovationsdW Ais (t) in addition to regulating

the rate of convergence.24 Comparative advantage reflects a double normalization of export capability—by

23This point is analogous to critiques of using cross-country regressions to test for convergence in rates of economic growth (seee.g. Quah 1996).

24Among possible parametrizations of the OU process, we choose (11) because it is closely related to our later extension to

20

the global industry-year and by the country-year. It is therefore natural to consider a global mean of one,

implying a global mean of zero forln Ais(t).

The OU process is the unique non-degenerate Markov process that has a stationary normal distribution

(Karlin and Taylor 1981, ch. 15, proposition 5.1).25 The OU process of log comparative advantageln Ais(t)

has therefore as its stationary distribution a log normal distribution of comparative advantageAis(t). In

other words, if we observed comparative advantageAis(t) and plotted it with graphs like those inFigure 2,

we would find a log normal shape if and only if the underlying Markov process of log comparative advantage

ln Ais(t) is an OU process. InFigure 2, we only observe absolute advantage, however, so it remains for us

to relate the two cross sectional distributions of comparative and absolute advantage.

In (11), we refer to the parameterη as therate of dissipationof comparative advantage because it

contributes to the speed with which log comparative advantage would collapse to a degenerate level of

zero in all industries and all countries if there were no stochastic innovations. The parametrization in (11)

implies thatη alone determines the shape and heavy tail of the resulting stationary distribution, whileσ is

irrelevant for the cross sectional distribution. Our parametrization is akin to a standardization by whichη

is a normalized rate of dissipation that measures the “number” of typical (one-standard deviation) shocks

that dissipate per unit of time. We refer to the parameterσ as theintensity of innovations. Under our

parametrization ofη, σ plays a dual role: on the one hand magnifying volatility by scaling up the Wiener

innovations and on the other hand contributing to the speed at which time elapses in the deterministic part

of the diffusion.

To connect the continuous-time OU process in (11) to our decay regression in (10), we use the fact

that the discrete-time process that results from sampling from an OU process at a fixed time interval∆ is a

Gaussian first-order autoregressive process with autoregressive parameterexp{−ησ2∆/2} and innovation

variance(1 − exp{−ησ2∆})/η (Aït-Sahalia et al. 2010, Example 13).26 Applying this insight to the first-

difference equation above, we obtain our decay regression:

lnAis(t+∆)− lnAis(t) = ρ lnAis(t) + δs(t) + εis(t, t+∆), (12)

a generalized logistic diffusion and because it clarifies that the parameterσ is irrelevant for the cross sectional distribution. Wedeliberately specify parametersη andσ that are invariant over time, industry and country and will explore the goodness of fit underthat restriction.

25The Ornstein-Uhlenbeck process is a continuous-time analogue to a mean reverting AR(1) process in discrete time. It is abaseline stochastic process in the natural sciences and finance (see e.g. Vasicek 1977, Chan et al. 1992).

26Concretely,ln Ais(t+∆) = exp{−ησ2∆/2} ln Ais(t) + εist(t, t+∆) for a disturbanceεist(t, t+∆) ∼ N (0, [1 −exp{−ησ2∆}]/η).

21

implying reduced-form expressions for the decay parameter

ρ ≡ −(1− exp{−ησ2∆/2}) < 0

and the unobserved fixed effectδs(t) ≡ lnZs(t+∆) − (1+ρ) lnZs(t), where the residualεist(t, t+∆)

is normally distributed with mean zero and variance(1 − exp{−ησ2∆})/η. An OU process withρ ∈

(0, 1) generates a log normal stationary distribution of absolute advantage in the cross section, with a shape

parameter of1/η and a mean of zero.

The estimated dissipation coefficientρ is a function both of the dissipation rateη and the intensity of

innovationsσ and therefore may vary across samples because either or both of these parameters vary. This

distinction is important becauseρ may change even though the heavy tail of the distribution of comparative

advantage does not. From OLS estimation of the decay regression in (12), we can obtain estimates ofη and

σ2 using the solutions,

η =1− (1 + ρ)2

s2

σ2 =s2

1− (1 + ρ)2ln (1 + ρ)−2

∆, (13)

whereρ is the estimated decay rate ands2 is the estimated variance of the decay regression residual.

Table 1 shows estimates ofη and σ2 implied by the decay regression results, with standard errors

obtained using the delta method. Across samples, the estimate ofη based on log absolute advantage is very

similar to that based on the log RCA index, implying that the two measures of comparative advantage have

a cross sectional distribution of similar shape. Patterns of interest emerge when we compareη andσ2 across

subsamples.

First, consider the subsample of developing economies in columns 3 and 4 ofTable 1 and compare the

estimates to those for the average country in the full sample (columns 1 and 2). The larger estimates ofρ

in absolute value imply that mean reversion is more rapid in the developing-country group. However, this

result is silent about any underlying country differences in the cross sectional distribution of comparative

advantage. We see that the estimated dissipation rateη among developing countries is not markedly different

from that in the average country; in fact theη estimates are not statistically significantly different from each

other for the exporter capability measurek. This similarity in the estimated dissipation rateη indicates that

comparative advantage is similarly heavy-tailed in the group of developing countries as in the sample of all

countries. The faster reduced-form decay rateρ for developing countries results mainly from their having

a larger intensity of innovationsσ. In other words, a typical comparative-advantage innovation (a one-

22

standard-deviation shock) in a developing country dissipates at roughly the same rate as in an industrialized

country but the typical innovation is larger in a developing country.

Second, we can compare non-manufacturing industries in columns 5 and 6 to the average industry in

columns 1 and 2. Whereas non-manufacturing industries differ considerably from the average industry in

measured decay ratesρ, there is no such marked difference in the estimated dissipation ratesη. For either

measure of comparative advantage, the dissipation rateη is more similar between a non-manufacturing in-

dustry and the average industry than the measured decay ratesρ would appear. This implies that comparative

advantage is similarly heavy-tailed among non-manufacturing industries as in the sample of all industries.

However, the intensity of innovations is much larger in non-manufacturing industries than in the average

industry, perhaps due to higher volatility in commodity output or commodity prices. These nuances regard-

ing the implied shape of, and the convergence speed towards, the cross sectional distribution of comparative

advantage are not apparent when one focuses only on the reduced-form decay rates themselves.

Finally, we compare results across two, three, and four-digit industries in AppendixTable A2 for the

subperiod 1984-2007 when a more detailed industry classification becomes available. Whereas reduced-

form decay ratesρ increase in magnitude as one goes from the two to four-digit level, dissipation ratesη

tend to move in the opposite direction and fall as one goes from the more aggregate to the more detailed

industry classification. For the exporter capability measure of comparative advantage, the drop inη between

the two and the four-digit level is not statistically significant in the full sample of industries and countries—

indicating intuitively that the shape of the cross sectional distribution of comparative advantage remains

similar at varying levels of industry aggregation.27 The difference in reduced-form decay ratesρ is largely

driven by a larger intensity of innovationsσ among the more narrowly defined industries at the four-digit

level.

The diffusion model in (11) and its discrete analogue in (12) reveal a deep connection between hyperspe-

cialization in exporting and churning in industry export ranks. Random innovations in absolute advantage

cause industries to alternate places in the cross sectional distribution of comparative advantage for a coun-

try, while the dissipation of absolute advantage creates a stable, heavy-tailed distribution of export prowess.

Having established a connection between hyperspecialization and industry churning, we turn next to a more

rigorous analysis of its origins.

27In the subsamples of less developed countries and non-manufacturing industries, however, the dissipation ratesη fall morepronounced as one goes from the more aggregate to the more detailed industry classification. Those findings imply that, in thosesubsamples, the cross sectional distribution of comparative advantage is more widely dispersed and thus more heavy tailed for themore detailed industry classification. Intuitively, at finer levels of aggregation, the few top industries carry more weight.

23

4 The Diffusion of Comparative Advantage

We now search in a more general setting for a parsimonious stochastic process that characterizes the dy-

namics of comparative advantage. In Figure 2, the cross-sectional distributions of absolute advantage drift

rightward perpetually, implying that absolute advantage is not stationary. However, the cross-sectional dis-

tributions preserve their shape over time. We therefore consider absolute advantage as a proportionally

scaled outcome of an underlying stationary and ergodic variable: comparative advantage. One candidate

stationary and ergodic variable is the Balassa RCA index because it removes a specific type of country-

wide trend. Instead of limiting ourselves to a narrowly imposed form, we specifygeneralized comparative

advantagein continuous time as

Ais(t) ≡Ais(t)

Zs(t), (14)

whereAis(t) is observed absolute advantage andZs(t) is an unobserved country-wide stochastic trend. It

follows directly that this measure satisfies the properties of the comparative advantage statistic in (3) that

compares individual country and industry pairs.

To find a well-defined stochastic process that is consistent with the churning of absolute advantage over

time and with heavy tails in the cross section, we implement a generalized logistic diffusion of comparative

advantageAis(t), which has a generalized gamma as its stationary distribution. Comparative advantage in

the cross section is then denoted withAis and understood to have a time-invariant distribution. Absolute

advantageAis(t), in contrast, has a trend-scaled generalized gamma as its cross-sectional distribution, with

stable shape but moving position as in Figure 2.28

The attractive feature of the generalized gamma is that it nests many distributions as special or limiting

cases, making the diffusion we employ flexible in nature. We construct a GMM estimator by working with a

mirror diffusion, which is related to the generalized logistic diffusion through an invertible transformation.

Our estimator uses the conditional moments of the mirror diffusion and accommodates the fact that we

observe absolute advantage only at discrete points in time. After estimating the stochastic process from the

time series of absolute advantage in Section 5, we explore how well the implied cross-sectional distribution

fits the actual cross-section data, which we do not target in estimation.

28In log terms, the non-stationary trend becomes an additive component that continually shifts the stationary distribution ofcomparative advantage:lnAis(t) = lnZs(t) + ln Ais.

24

4.1 Generalized logistic diffusion

The regularities in Section 3.1 indicate that the log normal distribution is a plausible benchmark distribution

for the cross section of absolute advantage.29 But the graphs inFigure 2 (and their companion graphs in

Figures A1 throughA3) also suggest that for many countries and years, the number of industries drops off

faster or more slowly in the upper tail than the log normal distribution can capture. We require a distribution

that generates kurtosis that is not simply a function of the lower-order moments, as would be the case in

the two-parameter log normal. The generalized gamma distribution, which unifies the gamma and extreme-

value distributions as well as many other distributions (Crooks 2010), offers a candidate family.30 Our

implementation of the generalized gamma uses three parameters, as in Stacy (1962).31

In a cross section of the data, after arbitrarily much time has passed, the proposed relevant generalized

gamma probability density function for a realizationais of the random variable comparative advantageAis

is given by:

fA(ais; θ, κ, φ) =1

Γ(κ)

∣

∣

∣

∣

φ

θ

∣

∣

∣

∣

(

ais

θ

)φκ−1

exp

{

−

(

ais

θ

)φ}

for ais > 0, (15)

whereΓ(·) denotes the gamma function and(θ, κ, φ) are real parameters withθ, κ > 0.32 The generalized

gamma nests as special cases, among several others, the ordinary gamma distribution forφ = 1 and the log

normal or Pareto distributions whenφ tends to zero.33 The parameter restrictionφ = 1 clarifies that the

generalized gamma distribution results when one takes an ordinary gamma distributed variable and raises it

to a finite power1/φ. The exponentiated random variable is then generalized gamma distributed, a result

that points to a candidate stochastic process that has a stationary generalized gamma distribution. The

ordinarylogistic diffusion, a widely used stochastic process, generates an ordinary gamma as its stationary

29A log normal distribution also approximates the firm size distribution reasonably well (Sutton 1997). For the United States,Axtell (2001) argues that a Pareto distribution offers a tight fit to firm sizes but also documents that, in the upper and lower tailsof the cumulative distribution, the data exhibit curvature consistent with a log normal distribution and at variance with a Paretodistribution.

30In their analysis of the firm size distribution by age, Cabral and Mata (2003) also use a version of the generalized gammadistribution with a support bounded below by zero and document a good fit.

31In the original Amoroso (1925) formulationthe generalized gamma distribution has four parameters. One of the four parametersis the lower bound of the support. However, our measure of absolute advantageAis can be arbitrarily close to zero by construction(because the exporter-industry fixed effect in gravity estimation is not bounded below so that by (7)logAis can be negative andarbitrarily small). As a consequence, the lower bound of the support is zero in our application. This reduces the relevant generalizedgamma distribution to a three-parameter function.

32We do not restrictφ to be strictly positive (as do e.g. Kotz et al. 1994, ch. 17). We allowφ to take any real value (see Crooks2010), including a strictly negativeφ for a generalized inverse gamma distribution. Crooks (2010) shows that this generalizedgamma distribution (Amoroso distribution) nests the gamma, inverse gamma, Fréchet, Weibull and numerous other distributions asspecial cases and yields the normal, log normal and Pareto distributions as limiting cases.

33As φ goes to zero, it depends on the limiting behavior ofκ whether a log normal distribution or a Pareto distribution results(Crooks 2010, Table 1).

25

distribution (Leigh 1968). By extension, thegeneralizedlogistic diffusion has ageneralizedgamma as its

stationary distribution.

Lemma 1. The generalized logistic diffusion

dAis(t)

Ais(t)=

σ2

2

[

1− ηAis(t)

φ − 1

φ

]

dt+ σ dWAis (t) (16)

for real parametersη, φ, σ has a stationary distribution that is generalized gamma with a probability density

fA(ais; θ, κ, φ) given by(15), forAis (understood to have a time-invariant cross sectional distribution) and

the real parameters

θ =(

φ2/η)1/φ

> 0 and κ = 1/θφ > 0.

A non-degenerate stationary distribution exists only ifη > 0.

Proof. See Appendix A.

The term(σ2/2)[1− η{Ais(t)φ − 1}/φ] in (16) is a deterministic drift that regulates the relative change in

comparative advantage dAis(t)/Ais(t). The variableW Ais (t) is the Wiener process. The generalized logistic

diffusion nests the Ornstein-Uhlenbeck process (φ→ 0), leading to a log normal distribution in the cross

section. In the estimation, we will impose the condition thatη > 0.34

The deterministic drift involves two types of components: constant parameters (η, φ, σ) on the one hand,

and a level-dependent componentAis(t)φ on the other hand, whereφ is the elasticity of the mean reversion

with respect to the current level of absolute advantage. We callφ the level elasticity of dissipation. The

ordinary logistic diffusion has a unitary level elasticity of dissipation (φ = 1). In our benchmark case of the

OU process (φ→ 0), the relative change in absolute advantage is neutral with respect to the current level. If

φ > 0, then the level-dependent drift componentAis(t)φ leads to a faster than neutral mean reversion from

above than from below the mean, indicating that the loss of absolute advantage tends to occur more rapidly

than elimination of absolute disadvantage. Conversely, ifφ < 0 then mean reversion tends to occur more

slowly from above than below the long-run mean, indicating that absolute advantage is sticky. Only in the

level neutral case ofφ → 0 is the rate of mean reversion from above and below the mean the same.

The parametersη andσ in the generalized logistic diffusion in (16) inherit their interpretations from the

OU process in (11) as the rate of dissipation and the intensity of innovations, respectively. The intensity

of innovationsσ again plays a dual role: on the one hand magnifying volatility by scaling up the Wiener

innovations and on the other hand regulating how fast time elapses in the deterministic part of the diffusion.

34If η where negative, comparative advantage would collapse over time forφ < 0 or explode forφ ≥ 0.

26

This dual role now guarantees that the diffusion will have a non-degenerate stationary distribution. Scaling

the deterministic part of the diffusion byσ2/2 ensures that stochastic deviations of comparative advantage

from the long-run mean do not persist and that dissipation occurs at precisely the right speed to offset the

unbounded random walk that the Wiener process would otherwise induce for each country-industry.

Under the generalized logistic diffusion, the dissipation rateη and dissipation elasticityφ jointly de-

termine the heavy tail of the cross sectional distribution of comparative advantage, with the intensity of

innovationsσ determining the speed of convergence to this distribution but having no effect on its shape.

For subsequent derivations, it is convenient to restate the generalized logistic diffusion (16) more com-

pactly in terms of log changes as,

d ln Ais(t) = −ησ2

2

Ais(t)φ − 1

φdt+ σ dWA

is (t),

which follows from (16) by Ito’s lemma.

4.2 The cross sectional distributions of comparative and absolute advantage

If comparative advantageAis(t) follows a generalized logistic diffusion by (16), then the stationary dis-

tribution of comparative advantage is a generalized gamma distribution with density (15) and parameters

θ =(

φ2/η)1/φ

> 0 andκ = 1/θφ > 0 by Lemma 1. From this stationary distribution of comparative ad-

vantageAis(t), we can infer the cross distribution of absolute advantageAis(t). Note that, by definition (14),

absolute advantage is not necessarily stationary because the stochastic trend may not be stationary.

Absolute advantage is related to comparative advantage through a country-wide stochastic trend by

definition (14). Plugging this definition into (15), we can infer that the probability density of absolute

advantage must be proportional to

fA(ais; θ, Zs(t), κ, φ) ∝

(

ais

θZs(t)

)φκ−1

exp

−

(

ais

θZs(t)

)φ

.

It follows from this proportionality that the probability density of absolute advantage must be a generalized

gamma distribution withθs(t) = θZs(t) > 0, which is time varying because of the stochastic trendZs(t).

We summarize these results in a lemma.

Lemma 2. If comparative advantageAis(t) follows a generalized logistic diffusion

d ln Ais(t) = −ησ2

2

Ais(t)φ − 1

φdt+ σ dWA

is (t) (17)

27

with real parametersη, σ, φ (η > 0), then the stationary distribution of comparative advantageAis(t) is

generalized gamma with the CDF

FA(ais; θ, φ, κ) = G

[

(

ais

θ

)φ

;κ

]

,

whereG[x;κ] ≡ γx(κ;x)/Γ(κ) is the ratio of the lower incomplete gamma function and the gamma func-

tion, and the cross sectional distribution of absolute advantageAis(t) is generalized gamma with the CDF

FA(ais; θs(t), φ, κ) = G

[

(

aisθs(t)

)φ

;κ

]

for the strictly positive parameters

θ =(

φ2/η)1/φ

, θs(t) = θZs(t) and κ = 1/θφ.

Proof. Derivations above establish that the cross sectional distributions are generalized gamma. The cumu-

lative distribution functions follow from Kotz et al. (1994, Ch. 17, Section 8.7).

The graphs inFigure 2 plot the frequency of industries, that is the probability1 − FA(a; θs(t), φ, κ)

times the total number of industries (I= 135), on the vertical axis against the level of absolute advantage

a (such thatA ≥ a) on the horizontal axis. Both axes have a log scale. Lemma 2 clarifies that a country-

wide stochastic trendZs(t) shifts log absolute advantage in the graph horizontally but the shape related

parametersφ andκ are not country specific if comparative advantage follows a diffusion with a common set

of three deep parametersθ, κ, φ worldwide.

Finally, as a prelude to the GMM estimation we note that ther-th raw moments of the ratiosais/θs(t)

andais/θ are

E

[(

aisθs(t)

)r]

= E

[(

ais

θ

)r]

=Γ(κ+ r/φ)

Γ(κ)

and identical because both[ais/θs(t)]1/φ and[ais/θ]1/φ have the same standard gamma distribution (Kotz

et al. 1994, Ch. 17, Section 8.7), whereΓ(·) denotes the gamma function. As a consequence, the raw

moments of absolute advantageAis are scaled by a country-specific time-varying factorZs(t)r whereas the

raw moments of comparative advantage are constant over time if comparative advantage follows a diffusion

with three constant deep parametersθ, κ, φ:

E [(ais)r|Zs(t)

r] = Zs(t)r · E [(ais)

r] = Zs(t)r · θr

Γ(κ+ r/φ)

Γ(κ).

28

By Lemma 2, the median of comparative advantage isa.5 = θ(G−1[.5;κ])1/φ. A measure of concentration

in the right tail is the ratio of the mean and the median (mean/median ratio), which is independent ofθ and

equals

Mean/median ratio=Γ(κ+ 1/φ)/Γ(κ)

(G−1[.5;κ])1/φ. (18)

We report this measure of concentration with our estimates to characterize the curvature of the stationary

distribution.

4.3 Implementation

The generalized logistic diffusion model (16) has no known closed form transition density whenφ 6= 0.

We therefore cannot evaluate the likelihood of the observed data and cannot perform maximum likelihood

estimation. However, an attractive feature of the generalized logistic diffusion is that it can be transformed

into a diffusion that belongs to the Pearson-Wong family, for which closed-form solutions of the condi-

tional moments exist.35 We construct a consistent GMM estimator based on the conditional moments of a

transformation of comparative advantage, using results from Forman and Sørensen (2008).

Our model depends implicitly on the unobserved stochastic trendZs(t). We use a closed form expression

for the mean of a log-gamma distribution to identify and concentrate out this trend. For a given country and

year, the cross-section of the data across industries has a generalized gamma distribution. The mean of the

log of this distribution can be calculated explicitly as a function of the model parameters, enabling us to

identify the trend from the relation thatEst[ln Ais(t)] = Est[lnAis(t)] − lnZs(t) by definition (14). We

adopt the convention that the expectations operatorEst[·] denotes the conditional expectation for source

countrys at timet. This result is summarized in the following proposition:

Proposition 1. If comparative advantageAis(t) follows the generalized logistic diffusion(16) with real

parametersη, σ, φ (η > 0), then the country specific stochastic trendZs(t) is recovered from the first

moment of the logarithm of absolute advantage as:

Zs(t) = exp

{

Est[lnAis(t)]−ln(φ2/η) + Γ′(η/φ2)/Γ(η/φ2)

φ

}

(19)

whereΓ′(κ)/Γ(κ) is the digamma function.

Proof. See Appendix B.

35Pearson (1895) first studied the family of distributions now called Pearson distributions. Wong (1964) showed that the Pearsondistributions are stationary distributions of a specific class of stochastic processes, for which conditional moments exist in closedform.

29

This proposition implies that for any GMM estimator, we can concentrate out the stochastic trend in

absolute advantage and work with an estimate of comparative advantage directly. Concretely, we obtain

detrended data based on the sample analog of equation (19):

AGMMis (t) = exp

lnAis(t)−1

I

I∑

j=1

lnAjs(t) +ln(φ2/η) + Γ′(η/φ2)/Γ(η/φ2)

φ

(20)

Detrending absolute advantage to arrive at an estimate of comparative advantage completes the first step in

implementing model (16).

Next, we perform a change of variable to recast our model as a Pearson-Wong diffusion. Rewriting

our model as a member of the Pearson-Wong family allows us to apply results in Kessler and Sørensen

(1999) and construct closed-form expressions for the conditional moments of comparative advantage. This

approach, introduced by Forman and Sørensen (2008), enables us to estimate the model using GMM.36 The

following proposition presents an invertible transformation of comparative advantage that makes estimation

possible.

Proposition 2. If comparative advantageAis(t) follows the generalized logistic diffusion(16) with real

parametersη, σ, φ (η > 0), then:

1. The transformed variable

Bis(t) = [Ais(t)−φ − 1]/φ (21)

follows the diffusion

dBis(t) = −σ2

2

[

(

η − φ2)

Bis(t)− φ]

dt+ σ

√

φ2Bis(t)2 + 2φBis(t) + 1 dWBis (t).

and belongs to the Pearson-Wong family.

2. For any timet, time interval∆ > 0, and integern ≤ M < η/φ2, then-th conditional moment of the

transformed processBis(t) satisfies the recursive condition:

E

[

Bis(t+∆)n∣

∣

∣Bis(t) = b

]

= exp {−an∆}n∑

m=0

πn,mbm−n−1∑

m=0

πn,mE

[

Bis(t+∆)m∣

∣

∣Bis(t) = b

]

(22)

where the coefficientsan andπn,m (n,m = 1, . . . ,M ) are defined in Appendix C.

36More generally, our approach fits into the general framework of prediction-based estimating functions reviewed in Sørensen(2011) and discussed in Bibby et al. (2010). These techniques have been previously applied in biostatistics (e.g., Forman andSørensen 2013) and finance (e.g., Lunde and Brix 2013).

30

Proof. See Appendix C.

Transformation (21) converts the diffusion of comparative advantageAis(t) into a mirror specification

that has closed form conditional moments. This central result enables us to construct a GMM estimator.

Consider time series observations forBis(t) at timest1, . . . , tT . By equation (22) in Proposition 2, we

can calculate a closed form for the conditional moments of the transformed diffusion at timetτ conditional

on the information set at timetτ−1. We then compute the forecast error based on using these conditional

moments to forecast them-th power ofBis(tτ ) with time tτ−1 information. These forecast errors must

be uncorrelated with any function of pastBis(tτ−1). We can therefore construct a GMM criterion for

estimation.

Denote the forecast error with

Uis(m, tτ−1, tτ ) = Bis(tτ )m − E

[

Bis(tτ )m∣

∣

∣Bis(tτ−1)

]

.

This random variable represents an unpredictable innovation in them-th power ofBis(tτ ). As a result,

Uis(m, tτ−1, tτ ) is uncorrelated with any measurable transformation ofBis(tτ−1). A GMM criterion func-

tion based on these forecast errors is

gis(φ, η, σ2) ≡

1

T − 1

T∑

τ=2

[h1(Bis(tτ−1))Uis(1, tτ−1, tτ ), . . . , hM (Bis(tτ−1))Uis(M, tτ−1, tτ )]′

where eachhm is a row vector of measurable functions specifying instruments for them-th moment condi-

tion. This criterion function is mean zero due to the orthogonality between the forecast errors and the time

tτ−1 instruments. Implementing GMM requires a choice of instruments. Computational considerations

lead us to choose polynomial vector instruments of the formhm(Bis(t)) = (1, Bis(t), . . . , Bis(t)K−1)′ to

constructK instruments for each of theM moments that we include in our GMM criterion.37

For observations fromI industries acrossS source countries, our GMM estimator solves the minimiza-

tion problem

(φ∗, η∗, σ2∗) = arg min(φ,η,σ2)

(

1

IS

∑

i

∑

s

gis(φ, η, σ2)

)′

W

(

1

IS

∑

i

∑

s

gis(φ, η, σ2)

)

for a given weighting matrixW .

37We work with a sub-optimal estimator because the optimal-instrument GMM estimator considered by Forman and Sørensen(2008) requires the inversion of a matrix for each observation. Given our large sample, this task is numerically expensive. Moreover,our ultimate GMM objective is ill-conditioned and optimization to find our estimates ofφ, η, andσ2 requires the use of an expensiveglobal numerical optimization algorithm. For these computational concerns we sacrifice efficiency and use sub-optimal instruments.

31

We evaluate this objective function at values ofφ, η, andσ2 by detrending the data to obtainAGMMis (t)

from equation (20), transforming these variables into their mirror variablesBGMMis (t) = [AGMM

is (t)−φ −

1]/φ, and using equation (22) to compute forecast errors. Then, we calculate the GMM criterion function

for each industry and country pair by multiplying these forecast errors by instruments constructed from

BGMMis (t), and finally sum over industries and countries to arrive at the value of the GMM objective.

For estimation we use two conditional moments and three instruments, leaving us with six equations

for three parameters. Being overidentified, we adopt a two-step estimator. On the first step we com-

pute an identity weighting matrix, which provides us with a consistent initial estimate. On the second

step we update the weighting matrix to an estimate of the optimal weighting matrix by settingW−1 =

(1/IS)∑

i

∑

s gis(φ, η, σ2)gis(φ, η, σ

2)′, which is calculated at the parameter value from the first step.

Forman and Sørensen (2008) establish asymptotics asT → ∞.38 We impose the constraints thatη > 0 and

σ2 > 0 by reparameterizing the model in terms ofln η > −∞ andln(σ2) > −∞, and use the delta method

to calculate standard errors for functions of the transformed parameters.

5 Estimates

Following the GMM procedure described in Section 4.3, we proceed to estimate the parameters for the

global diffusion of comparative advantage (η, σ, φ). It is worthy of note that, subject to a country-specific

stochastic trend, we are attempting to describe the global evolution of comparative advantage using just

three time-invariant parameters, which by implication must apply to all industries in all countries and in

all time periods. This approach contrasts sharply with our initial descriptive exercise inFigure 2, which

fits cumulative distribution plots to the log normal based on distribution parameters estimated separately

for each country and each year.Table 2 presents the estimation results. To verify that the results are not a

byproduct of specification error in estimating export capabilities from the gravity model, we also perform

GMM estimation using the Balassa (1965) RCA index.

The magnitude of the estimate ofη, which captures the dissipation of comparative advantage, is some-

what difficult to evaluate on its own. In its combination with the level elasticity of dissipationφ, η controls

both the magnitude of the long-run mean and the curvature of the cross-sectional distribution. The sign of

φ captures the stickiness of comparative advantage. The parameter estimate ofφ is robustly negative (and

38Our estimator would also fit into the standard GMM framework of Hansen (1982), which establishes consistency and asymp-totic normality of our estimator for the productIS → ∞. Given the dynamic nature of our times series exercise, we base theGMM weighting matrix and computations of standard errors on the asymptotics underT → ∞. Results under the alternativeasymptotics ofIS → ∞ are available from the authors upon request; those asymptotics tend to lead to less stable estimates acrossspecifications.

32

Table 2: GMM ESTIMATES OFCOMPARATIVE ADVANTAGE DIFFUSION

Full sample Subsamples: Absolute advantageAAbs. adv. Rev. adv. Exporter countries Sectors

A X LDC Non-LDC Manuf. Nonmanf.(1) (2) (3) (4) (5) (6)

Estimated Generalized Logistic Diffusion ParametersDissipation rateη 0.265 0.190 0.265 0.264 0.416 0.246

(0.004)∗∗ (.002)∗∗ (0.004)∗∗ (0.008)∗∗ (0.005)∗∗ (0.004)∗∗

Intensity of innovationsσ 1.396 1.189 1.587 0.971 1.157 1.625(0.039)∗∗ (.026)∗∗ (0.045)∗∗ (0.073)∗∗ (0.011)∗∗ (0.042)∗∗

Level elast. of dissipationφ -.034 -.030 -.027 -.036 -.064 -.028(0.004)∗∗ (.004)∗∗ (0.005)∗∗ (0.01)∗∗ (0.012)∗∗ (0.004)∗∗

Implied ParametersLog gen. gamma scaleln θ 160.7 177.8 223.8 146.4 72.6 201.6

(25.3)∗∗ (28.6)∗∗ (52.5)∗∗ (57.8)∗ (20.3)∗∗ (42.3)∗∗

Log gen. gamma shapelnκ 5.443 5.349 5.933 5.302 4.628 5.722(0.236)∗∗ (0.226)∗∗ (0.355)∗∗ (0.585)∗∗ (0.395)∗∗ (0.316)∗∗

Mean/median ratio 7.375 16.615 7.181 7.533 3.678 8.457

Obs. 459,680 459,680 296,060 163,620 230,890 228,790Root mean sq. forecast error 1.250 1.090 1.381 .913 1.022 1.409Min. GMM obj. (× 1,000) 0.411 0.012 1.040 1.072 0.401 0.440

Source: WTF (Feenstra et al. 2005, updated through 2008) for 135 time-consistent industries in 90 countries from 1962-2007 andCEPII.org; gravity-based measures of absolute advantage (7).Note: GMM estimation of the generalized logistic diffusion of comparative advantageAis(t),

d ln Ais(t) = −ησ2

2

Ais(t)φ − 1

φdt+ σ dW A

is (t),

using annual absolute advantage measuresAis(t) = Ais(t)Zs(t) on the full pooled sample (column 1) and subsamples (columns 3-6), and using the Balassa index of revealed comparative advantageXist = (Xist/

∑s′ Xis′t)/(

∑i′ Xi′st/

∑i′

∑s′ Xi′s′t)

instead of absolute advantage (column 2). Parametersη, σ, φ are estimated under the restrictionsln η, lnσ2 > −∞ for the mirrorPearson (1895) diffusion of (21), while concentrating out country-specific trendsZs(t). The implied parameters are inferred asθ = (φ2/η)1/φ, κ = 1/θφand the mean/median ratio is given by (18). Less developed countries (LDC) as listed in Appendix E.The manufacturing sector spans SITC one-digit codes 5-8, the nonmanufacturing merchandise sector codes 0-4. Standard errors inparentheses:∗ marks significance at five and∗∗ at one percent level. Standard errors of transformed and implied parameters arecomputed using the delta method.

33

precisely estimated), so we reject log normality in favor of the generalized gamma distribution. Negativity

in φ implies that comparative advantage reverts to the long-run mean more slowly from above than from

below. However, the value ofφ is not far from zero, suggesting that in practice deviations in comparative

advantage from log normality may be modest, as the plots inFigure 2 suggest.

The parameterσ regulates the intensity of innovations and captures both the volatility of the Wiener

innovations to comparative advantage and the a speed of convergence on the deterministic decay. This dual

role binds the parameter estimate ofσ to a level precisely such that a non-degenerate stationary distribution

exists. The intensity of innovations therefore does not play a role in determining the cross-sectional distribu-

tion’s shape. That job is performed byκ andθ, which exclusively depend onη andφ, so we are effectively

describing the shape of the cross-sectional distribution with just two parameters.

The parametersη andφ together imply a shape of the distribution with a strong concentration of ab-

solute and comparative advantage in the upper tail. The mean exceeds the median by a factor of more

than seven, both among developing and industrialized countries. This considerable concentration is mainly

driven by industries in the non-manufacturing merchandise sector, which exhibit a mean/median ratio of

more than eight (column 6), whereas the ratio is less than four for industries in the manufacturing sector

(column 5). When we use the Balassa (1965) RCA index, the mean/median ratio more than doubles to 16

(column 2). One interpretation of the greater concentration in revealed comparative advantage relative to

our geography-adjusted absolute advantage measure is that geography reinforces comparative advantage by

making countries appear overspecialized in the goods in which their underlying advantage is strong.

In Appendix Table A3 (to be included) we repeat the GMM procedure using data for the post-1984

period on SITC revision 2 industries at the two, three, or four-digit level. The results are largely in line with

those inTable 2. Estimates of the dissipation rateη are slightly larger for the post-1984 period than for the

full sample period, and, similar to what we found in the decay regressions inTable 1, become larger as one

moves from higher to lower levels of industry disaggregation. Estimates of the elasticity of dissipationφ are

negative in all cases except one—when we measure export prowess using log absolute advantage (based on

the gravity fixed effects) at the four-digit SITC level. As mentioned in Section 3.1, with nearly 700 four-

digit SITC rev. 2 industries we frequently have few destination markets per exporter-industry with which to

estimate the gravity fixed effects, contributing to noise in the estimated exporter-industry coefficients.

The parameters themselves give no indication of the fit of the model. To evaluate fit, we exploit the

fact that our GMM estimation targets exclusively the diffusion of comparative advantage—that is, the time

series behavior for country-industries—and not its cross-sectional dimension. Thus, the cross sectional

distribution of comparative advantage for a given country at a given moment in time provides a means of

34

validating our estimation procedure. For each country in each year, we project the cross sectional distribution

of comparative advantage implied by the parameters estimated from the diffusion and compare it to the

distribution based on the raw data.

To implement our validation exercise, we need a measure ofAist in equation (14), whose value depends

on Zst, the country-specific stochastic trend, which is unobserved. The role of the stochastic trend in the

diffusion is to account for horizontal shift in the distribution of log absolute advantage, which may result

from country-specific technological progress, factor accumulation, or other sources of aggregate growth. In

the estimation, we concentrate outZst by exploiting the fact that bothAist andAist have generalized gamma

distributions, allowing us to obtain closed-form solutions for their means, which isolates the value of the

stochastic trend. To obtain an empirical estimate ofZst at a given moment in time we apply equation (19),

which defines the variable as the difference between the mean log value ofAist and the expected value of

a log gamma distributed variable (which is a function ofη andφ). With estimated realizations for each

country in each year ofZst in hand, we compute realized values forAist for each country-industry in each

year.

To gauge the goodness of fit of our specification, we first plot our measure of absolute advantageAist.

To do so, following the earlier exercise inFigure 2, we rank order the data and plot for each country-

industry observation the level of absolute advantage (in log units) against the log number of industries with

absolute advantage greater than this value (which is given by the log of one minus the empirical CDF).

To obtain the simulated distribution resulting from the parameter estimates, we plot the global diffusion’s

implied stationary distribution for the same series. The diffusion implied values are constructed, for each

level ofAist, by evaluating the log of one minus the predicted generalized gamma CDF atAist = Aist/Zst.

The implied distribution thus uses the global diffusion parameter estimates as well as the identified country-

specific trendZst.

Figure 4 compares plots of the actual data against the diffusion implied plots for four countries in three

years, 1967, 1987, 2007.Figures A7, A8 andA9 in the Appendix present plots for the same 28 countries

in 1967, 1987 and 2007 as shown inFigures A1, A2 andA3 before. WhileFigures A1 throughA3 de-

picted Pareto and log normal maximum likelihood estimates of each individual country’s cross sectional

distribution by year (such that the number of parameters estimated equaled the number of parameters for

a distribution× number of countries× number of years), our exercise now is vastly more parsimonious

and based on a fit of the time-series evolution, not the observed cross sections.Figure 4 andFigures A7

throughA9 present the same, horizontally shifting but identically shaped, single cross-sectional distribution,

as implied by the two shape relevant parameter estimates (out of the three total) that fit the global diffusion

35

Figure 4: Global Diffusion Implied and Observed Cumulative Probability Distributions of AbsoluteAdvantage for Select Countries in 1967, 1987 and 2007

Brazil 1967 Brazil 1987 Brazil 2007

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

China 1967 China 1987 China 2007

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

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ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

Germany 1967 Germany 1987 Germany 2007

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128N

umbe

r of

Indu

strie

s

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

United States 1967 United States 1987 United States 2007

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

Source:WTF (Feenstra et al. 2005, updated through 2008) for 135 time-consistent industries in 90 countries from 1962-2007 andCEPII.org; gravity-based measures of absolute advantage (7).Note: The graphs show the observed and predicted frequency of industries (the cumulative probability1 − FA(a) times the totalnumber of industriesI = 135) on the vertical axis plotted against the level of absolute advantagea (such thatAist ≥ a) onthe horizontal axis. Both axes have a log scale. The predicted frequencies are based on the GMM estimates of the comparativeadvantage diffusion (17) in Table 2 (parametersη andphi in column 1) and the inferred country-specific stochastic trend componentlnZst from (19), which horizontally shifts the distributions but does not affect their shape.

36

for all country-industries and years. The country-specific trendZst terms shift the implied stationary distri-

bution horizontally, and we cut the depicted part of that single distribution at the lower and upper bounds of

the specific country’s observed support in a given year to clarify the fit.

Considering that the shape of the distribution effectively depends on only two parameters for all country-

industries and years, the simulated distributions fit the actual data remarkably well. There are important

differences between the actual and predicted plots in only a few countries and a few years, including China

in 1987, Russia in 1987 and 2007, Taiwan in 1987, and Vietnam in 1987 and 2007. Three of these four cases

involve countries undergoing a transition away from central planning during the designated time period,

suggesting periods of economic tumult.

There are some telling discrepancies between the actual and diffusion implied plots that are worthy

of further investigation. First, for some countries the upper tail of the distribution in the actual data plots

falls off more quickly than the predicted stationary distribution would imply. This suggests that for some

countries comparative advantage is relatively sticky (i.e., the true value ofφ for these countries may be

larger in absolute value than that shown inTable 2). However, a handful of countries in East and Southeast

Asia—China, Japan, Korea Rep., Malaysia, Taiwan, and Vietnam—show the opposite pattern. They exhibit

less concavity in the data than in the diffusion implied distribution, revealing less stickiness in comparative

advantage than the predicted stationary CDF would indicate, consistent with aφ that is smaller in absolute

value than inTable 2 or even positive. What remains unclear is whether these differences in fit across

countries are associated with the countries or with particular industries in these countries, an issue we will

explore in upcoming work.

Future empirical analysis in this paper will account for the following extensions.

1. We will use our estimates of the parameters of the generalized gamma distribution to simulate a

multi-sector version of the EK model. First, we will use the generalized gamma to generate location

parameters of the Fréchet distribution for firm productivity in each industry and in each country. We

will then combine these location parameters with values for preference and technology parameters

taken from the trade literature to simulate a global general equilibrium, which yields a gravity equa-

tion. Finally, we will add randomly generated noise to the “true” trade values and apply the gravity

model to estimate exporter-industry fixed effects on the simulated data plus noise. By comparing these

gravity estimates to our underlying generalized gamma draws of the location parameters, we can as-

sess the extent to which measurement error in trade data contaminates our measurement of country

export prowess.

2. We will examine alternative measures of the goodness of fit of the generalized logistic diffusion by (a)

37

plotting observed quantiles for absolute advantage against predicted quantiles for absolute advantage,

and (b) restricting the estimation to the latter half of the sample period and using these estimates to

simulate distributions for the first half of the sample period.

3. We will examine the robustness of our results to (a) using MPML-based estimates of gravity fixed

effects that account for zero flows, and (b) excluding industries (mainly in electronics, electrical ma-

chinery, transportation equipment, apparel, and footwear) in which global production networks figure

prominently and in which domestic value added accounts for a relatively small share of gross exports.

4. We will derive the exact discrete-time process that results from sampling from our generalized logistic

diffusion at a fixed time interval∆ and compute the precise decadal evanescence rate forφ 6= 0 and

∆ = 10 using the according generalized autoregressive parameter function of the exact discrete-time

process and evaluateρ at three percentiles of comparative advantage for the pooled sample as well as

by country and sector.

5. We will re-estimate the GMM specification by explicitly allowing the absolute advantage measures

Aist to be aggregates of trade events between the discrete points of observation Sørensen (2011),

beyond our current implementation of discrete-time trade events.

6 Conclusion

Two salient facts about comparative advantage arise from our investigation of trade flows among a large

set of countries and industries over more than four decades: While at any moment of time countries exhibit

hyperspecialization in only a few industries, the deviation in comparative advantage from its long-run global

mean dissipates at a brisk rate, of one-quarter to one-third over a decade. This impermanence implies that

the identity of the industries in which a country currently specializes changes considerably over time. Within

two decades, a country’s rising industries replace on average three of its top five initial industries in terms

of absolute advantage.

We specify a parsimonious stochastic process for comparative advantage with only three parameters by

generalizing the two-parameter logistic diffusion. The generalized logistic diffusion is consistent with both

hyperspecialization in the cross section and perpetual churning in industry export ranks. We additionally

allow for a country-specific stochastic trend whose removal translates absolute advantage into comparative

advantage and estimate the global parameters of the generalized logistic diffusion using a recently developed

GMM estimator for a well-defined mirror process. In this novel approach, we estimate the stochastic process

38

itself, rather than the repeated cross sections, and then use the two time-invariant diffusion parameters

that determine the shape of the cross-sectional distribution to assess the fit of the predicted cross-sectional

distribution across countries and over time. Even though our estimator does not target the cross sections—

but rather the annual diffusion—we find that the shape of the predicted stationary cross section tightly

matches the shape and curvature of the observed cross-sectional distributions for the bulk of countries and

years.

The exercises in this paper deliberately set aside questions about the deeper origin of comparative advan-

tage and aim instead to characterize the empirical evolution of comparative advantage in a typical country-

industry. In future research, we plan to explore natural follow-up questions.

1. We plan a systematic account of the country-industries whose evolution defies the global diffusion

in the sense that their rapid success or decline over time beats the odds and lies outside a confidence

bound of the likely evolution under the specified generalized logistic diffusion. Once the outside-

the-odds successes and failures are accounted for, we can ask whether their subsequent performance

remained outside the odds and what known market-driven forces or government interventions may

account for their beating the odds. In this context, we can explore the addition of a Lévy jump process

to our generalized logistic diffusion, generating a stationary distribution with no closed form, while

restricting parameters so that the implied stationary distribution approximates the generalized gamma

arbitrarily closely. The resulting stochastic process can potentially explain the evolution of individual

country-industries more completely.

2. We plan to bring firm-level evidence on the employment and sales concentration among exporting and

non-exporting firms in select countries to the project and thus complement our sector-level evidence

with recent advances in firm-level theories of international trade. Countries for which we have access

to firm-level data include Brazil, Germany and Sweden. Firms might withstand sector-level dissipa-

tion of comparative advantage by expanding their product scope across sectors or, alternatively, might

be subject to similar rates of dissipation as their home sector. Firm-level evidence can sharpen our

understanding of how the ongoing process of innovation in manufacturing industries and exploration

in non-manufacturing industries contribute to hyperspecialization and industry churning.

39

Appendix

A Generalized Logistic Diffusion: Proof of Lemma 1

The ordinary gamma distribution arises as the stationary distribution of the stochastic logistic equation(Leigh 1968). We generalize this ordinary logistic diffusion to yield a generalized gamma distribution asthe stationary distribution in the cross section. Note that the generalized (three-parameter) gamma distribu-tion relates to the ordinary (two-parameter) gamma distribution through a power transformation. Take anordinary gamma distributed random variableX with two parametersθ, κ > 0 and the density function

fX(x; θ, κ) =1

Γ(κ)

1

θ

(x

θ

)κ−1exp

{

−x

θ

}

for x > 0. (A.1)

Then the transformed variableA = X1/φ has a generalized gamma distribution under the accompanyingparameter transformationθ = θ1/φ because

fA(a; θ, κ, φ) = ∂∂a Pr(A ≤ a) = ∂

∂a Pr(X1/φ ≤ a)

= ∂∂a Pr(X ≤ aφ) = fX(aφ; θφ, κ) · |φaφ−1|

=aφ−1

Γ(κ)

∣

∣

∣

∣

φ

θφ

∣

∣

∣

∣

(

aφ

θφ

)κ−1

exp

{

−aφ

θφ

}

=1

Γ(κ)

∣

∣

∣

∣

φ

θ

∣

∣

∣

∣

(

a

θ

)φκ−1

exp

{

−

(

a

θ

)φ}

,

which is equivalent to the generalized gamma probability density function (15), whereΓ(·) denotes thegamma function andθ, κ, φ are the three parameters of the generalized gamma distribution in our context(a > 0 can be arbitrarily close to zero).

The ordinary logistic diffusion of a variableX follows the stochastic process

dX(t) =[

α− β X(t)]

X(t) dt+ σ X(t) dW (t) for X(t) > 0, (A.2)

whereα, β, σ > 0 are parameters,t denotes time,W (t) is the Wiener process (standard Brownian motion)and a reflection ensures thatX(t) > 0. The stationary distribution of this process (the limiting distributionof X = X(∞) = limt→∞X(t)) is known to be an ordinary gamma distribution (Leigh 1968):

fX(x; θ, κ) =1

Γ(κ)

∣

∣

∣

∣

1

θ

∣

∣

∣

∣

(x

θ

)κ−1exp

{

−x

θ

}

for x > 0, (A.3)

as in (A.1) with

θ = σ2/(2β) > 0, (A.4)

κ = 2α/σ2 − 1 > 0

under the restrictionα > σ2/2. The ordinary logistic diffusion can also be expressed in terms of infinitesi-mal parameters as

dX(t) = µX(X(t)) dt+ σX(X(t)) dW (t) for X(t) > 0,

whereµX(X) = (α− β X)X and σ2

X(X) = σ2X2.

40

Now consider the diffusion of the transformed variableA(t) = X(t)1/φ. In general, a strictly monotonetransformationA = g(X) of a diffusionX is a diffusion with infinitesimal parameters

µA(A) =1

2σ2X(X)g′′(X) + µX(X)g′(X) and σ2

A(A) = σ2X(X)g′(X)2

(see Karlin and Taylor 1981, Section 15.2, Theorem 2.1). Applying this general result to the specific mono-tone transformationA = X1/φ yields thegeneralized logistic diffusion:

dA(t) =[

α− βA(t)φ]

A(t) dt+ σA(t) dW(t) for A(t) > 0. (A.5)

with the parameters

α ≡

[

1− φ

2

σ2

φ2+

α

φ

]

, β ≡β

φ, σ ≡

σ

φ. (A.6)

The term−βA(t)φ now involves a power function and the parameters of the generalized logistic diffusioncollapse to the parameters of the ordinary logistic diffusion forφ = 1.

We infer that the stationary distribution ofA(∞) = limt→∞A(t) is a generalized gamma distributionby (15) and by the derivations above:

fA(a; θ, κ, φ) =1

Γ(κ)

∣

∣

∣

∣

φ

θ

∣

∣

∣

∣

(

a

θ

)φκ−1

exp

{

−

(

a

θ

)φ}

for x > 0,

with

θ = θ1/φ = [σ2/(2β)]1/φ = [φσ2/(2β)]1/φ > 0,

κ = 2α/σ2 − 1 = [2α/σ2 − 1]/φ > 0 (A.7)

by (A.4) and (A.6).Existence of a non-degenerate stationary distribution withθ, κ > 0 circumscribes how the parameters

of the diffusionα, β, σ andφ must relate to each other. A strictly positiveθ implies that sign(β) = sign(φ).Second, a strictly positiveκ implies that sign(α − σ2/2) = sign(φ). The latter condition is closely relatedto the requirement that absolute advantage neither collapse nor explode. If the level elasticity of dissipationφ is strictly positive (φ > 0) then, for the stationary probability densityfA(·) to be non-degenerate, theoffsetting constant drift parameterα needs to strictly exceed the variance of the stochastic innovations:α ∈ (σ2/2,∞). Otherwise absolute advantage would “collapse” as arbitrarily much time passes, implyingindustries die out. Ifφ < 0 then the offsetting positive drift parameterα needs to be strictly less than thevariance of the stochastic innovations:α ∈ (−∞, σ2/2); otherwise absolute advantage would explode.

Our preferred parametrization (16) of the generalized logistic diffusion in Lemma 1 is

dAis(t)

Ais(t)=

σ2

2

[

1− ηAis(t)

φ − 1

φ

]

dt+ σ dWAis (t)

for real parametersη, φ, σ. That parametrization can be related back to the parameters in (A.5) by settingα = (σ2/2) + β andβ = ησ2/(2φ). In this simplified formulation, the no-collapse and no-explosionconditions are satisfied for the single restriction thatη > 0. The reformulation in (16) also clarifies that onecan view our generalization of the drift term[Ais(t)

φ − 1]/φ as a conventional Box-Cox transformation ofAis(t) to model the level dependence.

41

The non-degenerate stationary distribution accommodates both the log normal and the Pareto distribu-tion as limiting cases. Whenφ → 0, bothα andβ tend to infinity; if β did not tend to infinity, a driftingrandom walk would result in the limit. A stationary log normal distribution requires thatα/β → 1, soα → ∞ at the same rate withβ → ∞ asφ → 0. For existence of a non-degenerate stationary distribution,in the benchmark case withφ → 0 we need1/α → 0 for the limiting distribution to be log normal. Incontrast, a stationary Pareto distribution with shape parameterp would require thatα = (2 − p)σ2/2 asφ → 0 (see e.g. Crooks 2010, Table 1; proofs are also available from the authors upon request).

B Trend Identification: Proof of Proposition 1

First, consider a random variableX which has a gamma distribution with scale parameterθ and shapeparameterκ. For any powern ∈ N we have

E [ln(Xn)] =

ˆ ∞

0ln(xn)

1

Γ(κ)

1

θ

(x

θ

)κ−1exp

{

−x

θ

}

dx

=n

Γ(κ)

ˆ ∞

0ln(θz)zκ−1e−zdz

= n ln θ +n

Γ(κ)

ˆ ∞

0ln(z)zκ−1e−zdz

= n ln θ +n

Γ(κ)

∂

∂κ

ˆ ∞

0zκ−1e−zdz

= n ln θ + nΓ′(κ)

Γ(κ)

whereΓ′(κ)/Γ(κ) is the digamma function.From Appendix A (Lemma 1) we know that raising a gamma random variable to the power1/φ creates

a generalized gamma random variableX1/φ with shape parametersκ andφ and scale parameterθ1/φ.Therefore

E

[

ln(X1/φ)]

=1

φE [lnX] =

ln(θ) + Γ′(κ)/Γ(κ)

φ

This result allows us to identify the country specific stochastic trendXs(t).For Ais(t) has a generalized gamma distribution acrossi for any givens andt with shape parametersφ

andη/φ2 and scale parameter(φ2/η)1/φ we have

Est

[

ln Ais(t)]

=ln(φ2/η) + Γ′(η/φ2)/Γ(η/φ2)

φ

From definition (14) andAis(t) = Ais(t)/Zs(t) we can infer thatEst[ln Ais(t)] = Est[lnAis(t)]− lnZs(t).Re-arranging and using the previous result forE[ln Ais(t) | s, t] gives

Zs(t) = exp

{

Est[lnAis(t)]−ln(φ2/η) + Γ′(η/φ2)/Γ(η/φ2)

φ

}

as stated in the text.

42

C Pearson-Wong Process: Proof of Proposition 2

For a random variableX with a standard logistic diffusion (theφ = 1 case), the Bernoulli transformation1/X maps the diffusion into the Pearson-Wong family (see e.g. Prajneshu 1980, Dennis 1989). We followup on that transformation with an additional Box-Cox transformation and applyBis(t) = [Ais(t)

−φ − 1]/φ

to comparative advantage, as stated in (21). DefineW Bis (t) ≡ −W A

is (t). ThenA−φis = φBis(t) + 1 and, by

Ito’s lemma,

dBis(t) = d

(

Ais(t)−φ − 1

φ

)

= −Ais(t)−φ−1 dAis(t) +

1

2(φ+ 1)Ais(t)

−φ−2(dAis(t))2

= −Ais(t)−φ−1

[

σ2

2

(

1− ηAis(t)

φ − 1

φ

)

Ais(t) dt+ σAis(t) dW Ais (t)

]

+1

2(φ+ 1)Ais(t)

−φ−2σ2Ais(t)2 dt

= −σ2

2

[(

1 +η

φ

)

Ais(t)−φ −

η

φ

]

dt− σAis(t)−φ dWA

is (t) +σ2

2(φ+ 1)Ais(t)

−φ dt

= −σ2

2

[(

η

φ− φ

)

Ais(t)−φ −

η

φ

]

dt− σAis(t)−φ dWA

is (t)

= −σ2

2

[(

η

φ− φ

)

(φBis(t) + 1)−η

φ

]

dt+ σ(φBis(t) + 1) dW Bis (t)

= −σ2

2

[

(

η − φ2)

Bis(t)− φ]

dt+ σ

√

φ2Bis(t)2 + 2φBis(t) + 1 dWBis (t).

The mirror diffusionBis(t) is therefore a Pearson-Wong diffusion of the form:

dBis(t) = −q(Bis(t)− B) dt+√

2q(aBis(t)2 + bBis(t) + c) dWBis (t)

whereq = (η − φ2)σ2/2, B = σ2φ/(2q), a = φ2σ2/(2q), b = φσ2/q, andc = σ2/(2q).To construct a GMM estimator based on this Pearson-Wong representation, we apply results in Forman

and Sørensen (2008) to construct closed form expressions for the conditional moments of the transformeddata and then use these moment conditions for estimation. This technique relies on the convenient structureof the Pearson-Wong class and a general result in Kessler and Sørensen (1999) on calculating conditionalmoments of diffusion processes using the eigenfunctions and eigenvalues of the diffusion’s infinitesimalgenerator.39

A Pearson-Wong diffusion’s drift term is affine and its dispersion term is quadratic. Its infinitesimalgenerator must therefore map polynomials to equal or lower order polynomials. As a result, solving foreigenfunctions and eigenvalues amounts to matching coefficients on polynomial terms. This key observationallows us to estimate the mirror diffusion of the generalized logistic diffusion model and to recover thegeneralized logistic diffusion’s parameters.

39For a diffusiondX(t) = µX(X(t)) dt+ σX(X(t)) dWX(t)

the infinitesimal generator is the operator on twice continuously differentiable functionsf defined byA(f)(x) = µX(x) d/dx+1

2σX(x)2 d2/dx2. An eigenfunction with associated eigenvalueλ 6= 0 is any functionh in the domain ofA satisfyingAh = λh.

43

Given an eigenfunction and eigenvalue pair(hs, λs) of the infinitesimal generator ofBis(t), we canfollow Kessler and Sørensen (1999) and calculate the conditional moment of the eigenfunction:

E

[

Bis(t+∆)∣

∣

∣Bis(t)

]

= exp {λst}h(Bis(t)). (C.8)

Since we can solve for polynomial eigenfunctions of the infinitesimal generator ofBis(t) by matchingcoefficients, this results delivers closed form expressions for the conditional moments of the mirror diffusionfor Bis(t).

To construct the coefficients of these eigen-polynomials, it is useful to consider the case of a generalPearson-Wong diffusionX(t). The stochastic differential equation governing the evolution ofX(t) musttake the form:

dX(t) = −q(X(t)− X) +√

2(aX(t)2 + bX(t) + c)Γ′(κ)/Γ(κ) dWX(t).

A polynomialpn(x) =∑n

m=0 πn,mxm is an eigenfunction of the infinitesimal generator of this diffusion ifthere is some associated eigenvalueλn 6= 0 such that

−q(x− X)

n∑

m=1

πn,mmxm−1 + θ(ax2 + bx+ c)

n∑

m=2

πn,mm(m− 1)xm−2 = λn

n∑

m=0

πn,mxm

We now need to match coefficients on terms.From thexn term, we must haveλn = −n[1− (n− 1)a]q. Next, normalize the polynomials by setting

πm,m = 1 and defineπm,m+1 = 0. Then matching coefficients to find the lower order terms amounts tobackward recursion from this terminal condition using the equation

πn,m =bm+1

am − anπn,m+1 +

km+2

am − anπn,m+2 (C.9)

with am ≡ m[1− (m− 1)a]q, bm ≡ m[X +(m− 1)b]q, andcm ≡ m(m− 1)cq. Focusing on polynomialswith order ofn < (1 + 1/a)/2 is sufficient to ensure thatam 6= an and avoid division by zero.

Using the normalization thatπn,n = 1, equation (C.8) implies a recursive condition for these conditionalmoments:

E [X(t+∆)n) |X(t) = x ] = exp{−an∆}n∑

m=0

πn,mxm −n−1∑

m=0

πn,mE [X(t+∆)m |X(t) = x ] .

We are guaranteed that these moments exist if we restrict ourselves to the firstN < (1 + 1/a)/2 moments.To arrive at the result in the second part of Proposition 2, set the parameters asqs = σ2(η − φ2)/2,

Xs = φ/(η − φ2), as = φ2/(η − φ2), bs = 2φ/(η − φ2), andcs = 1/(η − φ2). From these parameters,we can construct eigenvalues and their associated eigenfunctions using the recursive condition (C.9). Thesecoefficients correspond to those reported in equation (22).

In practice, it is useful to work with a matrix characterization of these moment conditions by stackingthe firstN moments in a vectorYis(t):

Π · E[

Yis(t+∆)∣

∣

∣Bis(t)

]

= Λ(∆) ·Π · Yis(t) (C.10)

with Yis(t) ≡ (1, Bis(t), . . . , Bis(t)M )′ and the matricesΛ(t) = diag(e−a1t, e−a2t, . . . , e−aM t) andΠ =

(π1, π2, . . . , πM )′, whereπm ≡ (πm,0, . . . , πm,m, 0, . . . , 0)′ for eachm = 1, . . . ,M . In our implementation

44

of the GMM criterion function based on forecast errors, we work with the forecast errors of the linearcombinationΠ · Yis(t) instead of the forecast errors forYis(t). Either estimator is numerically equivalentsince the matrixΠ is triangular by construction, and therefore invertible.

D Connection to Endogenous Growth Theory

Eaton and Kortum (1999, 2010) provide a stochastic foundation for Fréchet distributed productivity. Theirfundamental unit of analysis is an idea for a new variety. An idea is a blueprint to produce a variety of goodi with efficiency q (in a source countrys). Efficiency is the amount of output that can be produced witha unit of input when the idea is realized, and this efficiency is common to all countries where the varietybased on the idea is manufactured. Suppose an idea’s efficiencyq is the realization of a random variableQ drawn independently from a Pareto distribution with shape parameterθi and location parameter (lowerbound) q.40 Suppose further that ideas for goodi arrive in continuous time at momentt according to a

(non-homogeneous) Poisson process with a time-dependent rate parameter normalized toq−θiRis(t). InEaton and Kortum (2010, ch. 4), the rate parameter is a deterministic function of continuous time. In futureempirical implementation, we can also specify a stochastic process for the rate parameter, giving rise to aCox process for idea generation.

In this setup, the arrival rate of ideas with an efficiency of at leastq (Q ≥ q) is q−θiRis(t). If there is noforgetting, then the measure of ideasTis(t) expands continuously and, at a momentt, it will have reached alevel

Tis(t) =

ˆ t

−∞

R(τ) dτ.

As a consequence, at momentt the number of ideas about goodi with efficiencyQ ≥ q is distributed Poissonwith parameterq−θiTis(t). Moreover, the productivityq = max{q} of the most efficient idea at momentt has an extreme value Fréchet distribution with the cumulative distribution functionFQ(q;Tis(t), θi) =exp{−Tis(t) q

−θi}, whereTis(t) = qis(t)θi (Eaton and Kortum 2010, ch. 4). In Section 2 we suppressed

time dependency ofqis

to simplify notation.Similar to Grossman and Helpman (1991), we can specify a basic differential equation for the generation

of new ideas:dTis(t) = Ris(t) = ξis(t)λis(t)

χLis(t), (D.11)

whereξis(t) is research productivity in country-industryis, including the efficiency of exploration in thenon-manufacturing sector and the efficiency of innovation in manufacturing,λis(t) = LR

is(t)/Lis(t) is thefraction of employment in country-industryis devoted to research (exploration or innovation), the parameterχ ∈ (0, 1) reflects diminishing returns to scale (whereaschi = 1 in Grossman and Helpman 1991) andLis(t) is total employment in country-industryis at momentt.

The economic value of an idea in source countrys is the expected profitπis(t) from its global expectedsales in industryi. Given the independence of efficiency draws, the expected profitπis(t) is equal to thetotal profitΠs(t) generated in source countrys’s industryi relative to the current measure of ideasTis(t):

πis(t) =Πs(t)

Tis(t)=

δiXis(t)

Tis(t)=

δi1− δi

ws(t)LPis(t)

Tis(t),

whereXis(t) ≡∑

dXisd(t) are global sales (exports∑

d′ 6=sXisd′ plus domestic salesXiss) andδi is the

40The Pareto CDF is1− (q/qis)−θi . Eaton and Kortum (1999) speak of the “quality of an idea” when they refer to its efficiency.

45

fraction of industry-wide profits in industry-wide sales (for a related derivation see Eaton and Kortum 2010,ch. 7). Industry-wide expected profits vary by the type of competition. Under monopolistic competition,a CES elasticity of substitution in demandσi and the Pareto shape parameter of efficiencyθi imply δi =(σi − 1)/[θiσi] (Eaton and Kortum 2010, ch. 5). The final step follows because the wage bill of laboremployed in production must be equal to the sales not paid out as profits:ws(t)L

Pis(t) = (1− δi)Xis(t).

In equilibrium, the CES demand system implies a well defined price indexPs(t) for the economy as awhole, so the real value of the idea at any future dateτ is πis(τ)/Ps(τ) and, for a fixed interest rater, thereal net present value of the idea at momentt is

Vis(t)

Ps(t)=

ˆ ∞

texp{−r(τ − t)}

πis(τ)

Ps(τ)dτ.

The exact price indexes in a multi-industry and multi-country equilibrium remain to be derived (a single-industry equilibrium is derived in Eaton and Kortum 2010, ch. 5 and 6). To illustrate the optimality conditiondriving endogenous growth, we can considerVis(t) as given but we note that it will be a function ofTis(t)in general.

Each idea has a nominal value ofVis(t), so the total value of research output isξis(t)λis(t)χLis(t)Vis(t)

at momentt, and the marginal product of engaging an additional worker in research isχξis(t)λis(t)χ−1Vis(t).

A labor market equilibrium with some research therefore requires that

χξis(t)λis(t)χ−1Vis(t) = ws ⇐⇒ λis(t) =

(

χξis(t)Vis(t)

ws

)1

1−χ

.

The exploration of new ideas in non-manufacturing and the innovation of products in manufacturing there-fore follow the differential equation

dTis(t) = ξis(t)1

1−χ

(

χVis(t)

ws

)χ

1−χ

Lis(t)

by (D.11). The nominal value of an ideaVis(t) is a function ofTis(t) in general, so this is a non-degeneratedifferential equation. Eaton and Kortum (2010, ch. 7) derive a balanced growth path for the economy inthe single-industry case. By making research productivityξis(t) stochastic, we can generate a stochasticdifferential equation for the measure of ideasTis(t) and thus the Fréchet productivity positionq

is(t) =

Tis(t)1/θi .

E Classifications and Additional Evidence

In this appendix, we report country and industry classifications, as well as additional evidence to complementthe reported findings in the text.

E.1 Classifications

Our empirical analysis requires a time-invariant definition of less developed countries (LDC) and industri-alized countries (non-LDC). Given our data time span of more then four decades (1962-2007), we classifythe 90 economies, for which we obtain exporter capability estimates, by their relative status over the entiresample period.

46

In our classification, there are 28non-LDC: Australia, Austria, Belgium-Luxembourg, Canada, ChinaHong Kong SAR, Denmark, Finland, France, Germany, Greece,Ireland, Israel, Italy, Japan, Kuwait, Nether-lands, New Zealand, Norway, Oman, Portugal, Saudi Arabia, Singapore,Spain, Sweden, Switzerland, Trini-dad and Tobago, United Kingdom, United States.

The remaining 62 countries areLDC: Algeria, Argentina, Bolivia, Brazil, Bulgaria, Cameroon, Chile,China, Colombia, Costa Rica, Cote d’Ivoire, Cuba, Czech Rep., Dominican Rep., Ecuador, Egypt, El Sal-vador, Ethiopia, Ghana, Guatemala, Honduras, Hungary, India, Indonesia, Iran, Jamaica, Jordan, Kenya,Lebanon, Libya, Madagascar, Malaysia, Mauritius, Mexico, Morocco, Myanmar, Nicaragua, Nigeria, Pak-istan, Panama, Paraguay, Peru, Philippines, Poland, Korea Rep., Romania, Russian Federation, Senegal,South Africa, Sri Lanka, Syria, Taiwan, Thailand, Tunisia, Turkey, Uganda, United Rep. of Tanzania,Uruguay, Venezuela, Vietnam, Yugoslavia, Zambia.

We split the industries in our sample by broad sector. The manufacturing sector includes all industrieswith an SITC one-digit code between 5 and 8. The non-manufacturing merchandise sector includes indus-tries in the agricultural sector as well industries in the mining and extraction sectors and spans the SITCone-digit codes from 0 to 4.

E.2 Additional evidence

Table A1 shows the top two products in terms of normalized log absolute advantagelnAist for 28 of the90 exporting countries, using 1987 and 2007 as representative years. To obtain a measure of comparativeadvantage, we normalize log absolute advantage by its country mean:lnAist − (1/I)

∑Ii′ lnAi′st. The

country normalization of log absolute advantagelnAist results in a double log difference of export capabilitykist—a country’s log deviation from the global industry mean in export capability minus its average logdeviation across all industries.

Table A2 presents estimates of the decay equation (10) for the period 1984-2007 using data from theSITC revision 2 sample. This recent sample allows us to perform regressions for log absolute advantage andthe log RCA index at the two, three and four-digit level. Estimated decay rates are comparable to those inTable 1, which uses data for the full period 1962-2007 at the level of 135 STIC three-digit industries.

Figures A1, A2andA3 extendFigure 2 in the text and plot, for 28 countries in 1967, 1987 and 2007,the log number of a source countrys’s industries that have at least a given level of absolute advantagein year t against that log absolute advantage levellnAist for industriesi. The figures also graph the fitof absolute advantage in the cross section to a Pareto distribution and to a log normal distribution usingmaximum likelihood, where each cross sectional distribution is fit separately for each country in each year(such that the number of parameters estimated equals the number of parameters for a distribution× numberof countries× number of years).

To verify that the graphed cross sectional distributions inFigures A1, A2 andA3 are not a byproductof specification error in estimating export capabilities from the gravity model, we repeat the plots using therevealed comparative advantage index by Balassa (1965).Figures A4, A5 andA6 plot, for the same 28countries in 1967, 1987 and 2007, the log number of a source countrys’s industries that have at least agiven level of revealed comparative advantage(Xis/

∑

s′ Xis′)/(∑

i′ Xi′s/∑

i′∑

s′ Xi′s′) in yeart againstthat comparative advantage level for industriesi. The figures also graph the fit of the revealed comparativeadvantage index in the cross section to a log normal distribution using maximum likelihood separately foreach country in each year.

Figures A7, A8andA9 extendFigure 4 in the text and plot, for 28 countries in 1967, 1987 and 2007, theobserved log number of a source countrys’s industries that have at least a given level of absolute advantagein year t against that log absolute advantage levellnAist for industriesi. This raw data plot is identical

47

Table A1:Top Two Industries by Normalized Absolute Advantage

Country 1987 2007 Country 1987 2007Argentina Maize, unmilled 5.13 Maize, unmilled 5.50 Mexico Sulphur 3.73 Alcoholic beverages 3.97

Animal feed 3.88 Oil seed 4.61 Crude minerals 3.26 Office machines 3.82

Australia Wool 4.15 Cheese & curd 3.25 Peru Metal ores & conctr. 4.24 Metal ores & conctr. 6.25Jute 3.83 Fresh meat 3.20 Animal feed 4.03 Coffee 4.60

Brazil Coffee 3.34 Iron ore 5.18 Philippines Vegetable oils & fats 3.81 Office machines 4.41Iron ore 3.21 Fresh meat 4.42 Pres. fruits & nuts 3.50 Electric machinery 3.51

Canada Sulphur 4.04 Wheat, unmilled 5.13 Poland Barley, unmilled 5.68 Furniture 3.07Pulp & waste paper 3.36 Sulphur 3.31 Sulphur 3.35 Glassware 2.74

China Explosives 7.05 Sound/video recorders 4.93 Korea Rep. Radio receivers 5.51 Television receivers 6.06Jute 4.24 Radio receivers 4.65 Television receivers 5.37 Telecomm. equipment 5.11

Czech Rep. Glassware 4.05 Glassware 4.17 Romania Furniture 3.55 Footwear 3.49Prep. cereal & flour 3.68 Road vehicles 3.58 Fertilizers, manuf. 2.73 Silk 3.15

Egypt Cotton 4.52 Fertilizers, crude 4.45 Russia Pulp & waste paper 5.16 Animal oils & fats 8.32Textile yarn, fabrics 2.90 Rice 3.91 Radioactive material 5.02 Fertilizers, manuf. 4.54

France Electric machinery 3.44 Oth. transport eqpmt. 3.31 South Africa Stone, sand & gravel 3.92 Iron & steel 4.17Alcoholic beverages 3.39 Alcoholic beverages 3.15 Radioactive material 3.65 Fresh fruits & nuts 3.47

Germany Road vehicles 3.95 Road vehicles 3.10 Taiwan Explosives 4.41 Television receivers 5.18General machinery 3.89 Metalworking machinery 2.70 Footwear 4.39 Office machines 5.01

Hungary Margarine 3.19 Telecomm. equipment 4.15 Thailand Rice 4.81 Rice 4.92Fresh meat 2.76 Office machines 4.08 Fresh vegetables 4.08 Natural rubber 4.50

India Tea 4.20 Precious stones 3.86 Turkey Fresh vegetables 3.48 Glassware 3.30Leather 3.90 Rice 3.61 Tobacco unmanuf. 3.41 Textile yarn, fabrics 3.20

Indonesia Natural rubber 5.10 Natural rubber 5.26 United States Office machines 3.96 Oth. transport eqpmt. 3.46Improved wood 4.74 Sound/video recorders 4.90 Oth. transport eqpmt. 3.25 Photographic supplies 2.60

Japan Sound/video recorders 6.28 Sound/video recorders 5.90 United Kingd. Measuring instrmnts. 3.20 Alcoholic beverages 3.26Road vehicles 6.08 Road vehicles 5.63 Office machines 3.15 Pharmaceutical prod. 3.12

Malaysia Natural rubber 6.19 Radio receivers 5.78 Vietnam Cereal meals & flour 5.34 Animal oils & fats 10.31Vegetable oils & fats 4.85 Sound/video recorders 5.03 Jute 5.14 Footwear 7.02

Source: WTF (Feenstra et al. 2005, updated through 2008) for 135 time-consistent industries in 90 countries from 1962-2007.Note: Top two industries for 28 of the 90 countries in 1987 and 2007 in terms of normalized log absolute advantage, relative to the country mean:lnAist − (1/I)

∑Ii′ lnAi′st.

48

Table A2: DECAY REGRESSIONS FORCOMPARATIVE ADVANTAGE AT VARYING LEVELS OF INDUSTRY

AGGREGATIONExporter capabilityk Balassa RCAln X

SITC aggregate 4 digit 3 digit 2 digit 4 digit 3 digit 2 digit(1) (2) (3) (4) (5) (6)

Panel A: Full sampleDecay rateρ -0.365 -0.241 -0.188 -0.323 -0.288 -0.256

(0.034)∗∗ (0.021)∗∗ (0.020)∗∗ (0.014)∗∗ (0.014)∗∗ (0.015)∗∗

Dissipation rateη 0.119 0.122 0.125 0.113 0.130 0.157(0.009)∗∗ (0.009)∗∗ (0.012)∗∗ (0.004)∗∗ (0.005)∗∗ (0.008)∗∗

Innovation intensityσ2 0.766 0.451 0.333 0.693 0.523 0.377(0.035)∗∗ (0.012)∗∗ (0.008)∗∗ (0.013)∗∗ (0.010)∗∗ (0.008)∗∗

Obs. 142,664 61,280 19,815 146,644 61,577 19,815Adj. R2 0.142 0.142 0.160 0.121 0.129 0.132

Panel B: LDC exportersDecay rateρ -0.503 -0.326 -0.236 -0.369 -0.336 -0.296

(0.045)∗∗ (0.032)∗∗ (0.028)∗∗ (0.017)∗∗ (0.016)∗∗ (0.016)∗∗

Dissipation rateη 0.113 0.122 0.121 0.099 0.115 0.138(0.007)∗∗ (0.010)∗∗ (0.013)∗∗ (0.004)∗∗ (0.005)∗∗ (0.007)∗∗

Innovation intensityσ2 1.235 0.646 0.446 0.927 0.711 0.508(0.086)∗∗ (0.027)∗∗ (0.016)∗∗ (0.022)∗∗ (0.016)∗∗ (0.012)∗∗

Obs. 79,325 37,918 13,167 81,963 38,095 13,167Adj. R2 0.168 0.156 0.165 0.132 0.136 0.137

Panel C: Non-manufacturing industriesDecay rateρ -0.530 -0.309 -0.251 -0.334 -0.287 -0.257

(0.046)∗∗ (0.027)∗∗ (0.026)∗∗ (0.015)∗∗ (0.015)∗∗ (0.015)∗∗

Dissipation rateη 0.095 0.111 0.146 0.086 0.114 0.157(0.005)∗∗ (0.008)∗∗ (0.013)∗∗ (0.003)∗∗ (0.005)∗∗ (0.008)∗∗

Innovation intensityσ2 1.591 0.665 0.397 0.945 0.597 0.379(0.118)∗∗ (0.024)∗∗ (0.014)∗∗ (0.019)∗∗ (0.013)∗∗ (0.009)∗∗

Obs. 37,645 17,985 7,482 40,472 18,236 7,482Adj. R2 0.176 0.133 0.133 0.124 0.140 0.164

Source: WTF (Feenstra et al. 2005, updated through 2008) for two-digit (61 industries), three-digit (227 industries), and four-digit(684 industries) sector definitions from 1984-2007, and CEPII.org.Note: Reported figures for five-year decadalized changes. Variables are OLS-estimated gravity measures of export capabilitykby (5) and the log Balassa index of revealed comparative advantageln Xist = ln(Xist/

∑s′ Xis′t)/(

∑i′ Xi′st/

∑i′

∑s′ Xi′s′t).

OLS estimation of the decadal decay rateρ from

kis,t+10 − kist = ρ kist + δit + δst + εist,

conditional on industry-year and source country-year effectsδit and δst for the full pooled sample (panel A) and subsamples(panels B and C). The implied dissipation rateη and innovation intensityσ2 are based on the decadal decay rate estimateρ andthe estimated variance of the decay regression residuals2 by (13). Less developed countries (LDC) as listed in Appendix E.Nonmanufacturing merchandise spans SITC sector codes 0-4. Standard errors (reported below coefficients) forρ are clustered bycountry and forη andσ are calculated using the delta method;∗∗ indicates significance at the 1% level.

49

to that inFigures A1 throughA3 and shown for the same 28 countries and years as before. In addition,Figures A7 throughA9 now plot the implied stationary distribution based on the time series diffusionestimates in Table 2 for the full sample (column 1), using the estimates of the two shape relevant globaldiffusion parameters (ηandφ), which determine the curvature of the implied single stationary distributionof comparative advantageAist (throughκ andφ), and the recovered estimates of the unknown country-widestochastic trendsZst, which determine the horizontal position of the stationary distribution of observedabsolute advantageAist.

50

Figure A1:Cumulative Probability Distribution of Absolute Advantage for 28 Countries in 1967

Argentina Australia Brazil Canada China Czech Rep. Egypt

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France Germany Hungary India Indonesia Japan Korea Rep.

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Malaysia Mexico Peru Philippines Poland Romania Russia

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South Africa Taiwan Thailand Turkey United Kingdom United States Vietnam

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Source:WTF (Feenstra et al. 2005, updated through 2008) for 135 time-consistent industries in 90 countries from 1962-2007 and CEPII.org; gravity-based measures of absoluteadvantage (7).Note: The graphs show the frequency of industries (the cumulative probability1 − FA(a) times the total number of industriesI = 135) on the vertical axis plotted against thelevel of absolute advantagea (such thatAist ≥ a) on the horizontal axis. Both axes have a log scale. The fitted Pareto and log normal distributions for absolute advantageAist

are based on maximum likelihood estimation by countrys in yeart = 1967.

51

Figure A2:Cumulative Probability Distribution of Absolute Advantage for 28 Countries in 1987

Argentina Australia Brazil Canada China Czech Rep. Egypt

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of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

Malaysia Mexico Peru Philippines Poland Romania Russia

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

South Africa Taiwan Thailand Turkey United Kingdom United States Vietnam

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

Source:WTF (Feenstra et al. 2005, updated through 2008) for 135 time-consistent industries in 90 countries from 1962-2007 and CEPII.org; gravity-based measures of absoluteadvantage (7).Note: The graphs show the frequency of industries (the cumulative probability1 − FA(a) times the total number of industriesI = 135) on the vertical axis plotted against thelevel of absolute advantagea (such thatAist ≥ a) on the horizontal axis. Both axes have a log scale. The fitted Pareto and log normal distributions for absolute advantageAist

are based on maximum likelihood estimation by countrys in yeart = 1987.

52

Figure A3:Cumulative Probability Distribution of Absolute Advantage for 28 Countries in 2007

Argentina Australia Brazil Canada China Czech Rep. Egypt

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

France Germany Hungary India Indonesia Japan Korea Rep.

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

Malaysia Mexico Peru Philippines Poland Romania Russia

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

South Africa Taiwan Thailand Turkey United Kingdom United States Vietnam

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Pareto Fit Log−Normal Fit

Source:WTF (Feenstra et al. 2005, updated through 2008) for 135 time-consistent industries in 90 countries from 1962-2007 and CEPII.org; gravity-based measures of absoluteadvantage (7).Note: The graphs show the frequency of industries (the cumulative probability1 − FA(a) times the total number of industriesI = 135) on the vertical axis plotted against thelevel of absolute advantagea (such thatAist ≥ a) on the horizontal axis. Both axes have a log scale. The fitted Pareto and log normal distributions for absolute advantageAist

are based on maximum likelihood estimation by countrys in yeart = 2007.

53

Figure A4:Cumulative Probability Distribution of Absolute Advantage for 28 Countries in 1967

Argentina Australia Brazil Canada China Czech Rep. Egypt

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

France Germany Hungary India Indonesia Japan Korea Rep.

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

Malaysia Mexico Peru Philippines Poland Romania Russia

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

South Africa Taiwan Thailand Turkey United Kingdom United States Vietnam

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

Source:WTF (Feenstra et al. 2005, updated through 2008) for 135 time-consistent industries in 90 countries from 1962-2007.Note: The graphs show the frequency of industries (the cumulative probability1 − FX(x) times the total number of industriesI = 135) on the vertical axis plotted against theBalassa index of revealed comparative advantageX = (Xis/

∑s′ Xis′)/(

∑i′ Xi′s/

∑i′

∑s′ Xi′s′) on the horizontal axis. Both axes have a log scale. The fitted log normal

distribution is based on maximum likelihood estimation by countrys in yeart = 1967.

54

Figure A5:Cumulative Probability Distribution of Absolute Advantage for 28 Countries in 1987

Argentina Australia Brazil Canada China Czech Rep. Egypt

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

France Germany Hungary India Indonesia Japan Korea Rep.

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

Malaysia Mexico Peru Philippines Poland Romania Russia

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

South Africa Taiwan Thailand Turkey United Kingdom United States Vietnam

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

Source:WTF (Feenstra et al. 2005, updated through 2008) for 135 time-consistent industries in 90 countries from 1962-2007.Note: The graphs show the frequency of industries (the cumulative probability1 − FX(x) times the total number of industriesI = 135) on the vertical axis plotted against theBalassa index of revealed comparative advantageX = (Xis/

∑s′ Xis′)/(

∑i′ Xi′s/

∑i′

∑s′ Xi′s′) on the horizontal axis. Both axes have a log scale. The fitted log normal

distribution is based on maximum likelihood estimation by countrys in yeart = 1987.

55

Figure A6:Cumulative Probability Distribution of Absolute Advantage for 28 Countries in 2007

Argentina Australia Brazil Canada China Czech Rep. Egypt

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

France Germany Hungary India Indonesia Japan Korea Rep.

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

Malaysia Mexico Peru Philippines Poland Romania Russia

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

South Africa Taiwan Thailand Turkey United Kingdom United States Vietnam

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries)

.01 .1 1 10 100Absolute Advantage

Data Log−Normal Fit

Source:WTF (Feenstra et al. 2005, updated through 2008) for 135 time-consistent industries in 90 countries from 1962-2007.Note: The graphs show the frequency of industries (the cumulative probability1 − FX(x) times the total number of industriesI = 135) on the vertical axis plotted against theBalassa index of revealed comparative advantageX = (Xis/

∑s′ Xis′)/(

∑i′ Xi′s/

∑i′

∑s′ Xi′s′) on the horizontal axis. Both axes have a log scale. The fitted log normal

distribution is based on maximum likelihood estimation by countrys in yeart = 2007.

56

Figure A7:Global Diffusion Implied and Observed Cumulative Probability Distributions of Absolute Advantage in 1967

Argentina Australia Brazil Canada China Czech Rep. Egypt

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

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ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

France Germany Hungary India Indonesia Japan Korea Rep.

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

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64

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Num

ber

of In

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ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

Malaysia Mexico Peru Philippines Poland Romania Russia

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

South Africa Taiwan Thailand Turkey United Kingdom United States Vietnam

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

Source:WTF (Feenstra et al. 2005, updated through 2008) for 135 time-consistent industries in 90 countries from 1962-2007 and CEPII.org; gravity-based measures of absoluteadvantage (7).Note: The graphs show the observed and predicted frequency of industries (the cumulative probability1 − FA(a) times the total number of industriesI = 135) on the verticalaxis plotted against the level of absolute advantagea (such thatAist ≥ a) on the horizontal axis, for the yeart = 1967. Both axes have a log scale. The predicted frequenciesare based on the GMM estimates of the comparative advantage diffusion (17) in Table 2 (parametersη andphi in column 1) and the inferred country-specific stochastic trendcomponentlnZst from (19), which horizontally shifts the distributions but does not affect their shape.

57

Figure A8:Global Diffusion Implied and Observed Cumulative Probability Distributions of Absolute Advantage in 1987

Argentina Australia Brazil Canada China Czech Rep. Egypt

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

France Germany Hungary India Indonesia Japan Korea Rep.

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

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16

32

64

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ber

of In

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ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

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ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

Malaysia Mexico Peru Philippines Poland Romania Russia

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

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ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

South Africa Taiwan Thailand Turkey United Kingdom United States Vietnam

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

Source:WTF (Feenstra et al. 2005, updated through 2008) for 135 time-consistent industries in 90 countries from 1962-2007 and CEPII.org; gravity-based measures of absoluteadvantage (7).Note: The graphs show the observed and predicted frequency of industries (the cumulative probability1 − FA(a) times the total number of industriesI = 135) on the verticalaxis plotted against the level of absolute advantagea (such thatAist ≥ a) on the horizontal axis, for the yeart = 1987. Both axes have a log scale. The predicted frequenciesare based on the GMM estimates of the comparative advantage diffusion (17) in Table 2 (parametersη andphi in column 1) and the inferred country-specific stochastic trendcomponentlnZst from (19), which horizontally shifts the distributions but does not affect their shape.

58

Figure A9:Global Diffusion Implied and Observed Cumulative Probability Distributions of Absolute Advantage in 2007

Argentina Australia Brazil Canada China Czech Rep. Egypt

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

France Germany Hungary India Indonesia Japan Korea Rep.

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

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ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

Malaysia Mexico Peru Philippines Poland Romania Russia

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

South Africa Taiwan Thailand Turkey United Kingdom United States Vietnam

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

1

2

4

8

16

32

64

128

Num

ber

of In

dust

ries

.01 .1 1 10 100Absolute Advantage

Data Fit Implied by Global Diffusion

Source:WTF (Feenstra et al. 2005, updated through 2008) for 135 time-consistent industries in 90 countries from 1962-2007 and CEPII.org; gravity-based measures of absoluteadvantage (7).Note: The graphs show the observed and predicted frequency of industries (the cumulative probability1 − FA(a) times the total number of industriesI = 135) on the verticalaxis plotted against the level of absolute advantagea (such thatAist ≥ a) on the horizontal axis, for the yeart = 2007. Both axes have a log scale. The predicted frequenciesare based on the GMM estimates of the comparative advantage diffusion (17) in Table 2 (parametersη andphi in column 1) and the inferred country-specific stochastic trendcomponentlnZst from (19), which horizontally shifts the distributions but does not affect their shape.

59

References

Abowd, John M., Robert H. Creecy, and Francis Kramarz, “Computing Person and Firm Effects UsingLinked Longitudinal Employer-Employee Data,”LEHD Technical Paper, March 2002,2002-06.

Aït-Sahalia, Yacine, Lars P. Hansen, and José A. Scheinkman, “Operator Methods for Continuous-TimeMarkov Processes,” in Yacine Aït-Sahalia and Lars P. Hansen, eds.,Handbook of Financial Econometrics,Vol. 1 of Handbooks in Finance, Amsterdam: North-Holland/Elsevier, 2010, chapter 1, pp. 1–66.

Amoroso, Luigi, “Ricerche Intorno alla Curva dei Redditi,”Annali di Matematica Pura ed Applicata, De-cember 1925,2 (1), 123–159.

Anderson, James E., “A Theoretical Foundation for the Gravity Equation,”American Economic Review,March 1979,69 (1), 106–16.

, “The Gravity Model,”Annual Review of Economics, 2011,3 (1), 133–60.

and Eric van Wincoop, “Gravity with Gravitas: A Solution to the Border Puzzle,”American EconomicReview, March 2003,93 (1), 170–92.

Arkolakis, Costas, Arnaud Costinot, and Andrés Rodríguez-Clare, “New Trade Models, Same OldGains?,”American Economic Review, February 2012,102(1), 94–130.

Armington, Paul S., “A Theory of Demand for Products Distinguished by Place of Production,”Interna-tional Monetary Fund Staff Papers, March 1969,16 (1), 159–178.

Axtell, Robert L., “Zipf Distribution of U.S. Firm Sizes,”Science, September 2001,293(5536), 1818–20.

Balassa, Bela, “Trade Liberalization and Revealed Comparative Advantage,”Manchester School of Eco-nomic and Social Studies, May 1965,33, 99–123.

Bhagwati, Jagdish, “Free Trade: Old and New Challenges,”Economic Journal, March 1994,104 (423),231–46.

Bibby, Bo M., Martin Jacobsen, and Michael Sørensen, “Estimating Functions for Discretely SampledDiffusion-Type Models,” in Yacine Aït-Sahalia and Lars P. Hansen, eds.,Handbook of Financial Econo-metrics, Vol. 1 ofHandbooks in Finance, Amsterdam: North-Holland/Elsevier, 2010, chapter 4, pp. 203–268.

Bombardini, Matilde, Giovanni Gallipoli, and German Pupato, “Skill Dispersion and Trade Flows,”American Economic Review, August 2012,102(5), 2327–48.

Cabral, Luís M. B. and José Mata, “On the Evolution of the Firm Size Distribution: Facts and Theory,”American Economic Review, September 2003,93 (4), 1075–1090.

Cadot, Olivier, Celine Carrére, and Vanessa Strauss Kahn, “Export Diversification: What’s behind theHump?,”Review of Economics and Statistics, May 2011,93 (2), 590–605.

Chan, K. C., G. Andrew Karolyi, Francis A. Longstaff, and Anthony B. Sanders, “An Empirical Com-parison of Alternative Models of the Short-Term Interest Rate,”Journal of Finance, July 1992,47 (3),1209–27.

60

Chor, Davin, “Unpacking Sources of Comparative Advantage: A Quantitative Approach,”Journal of Inter-national Economics, November 2010,82 (2), 152–67.

Costinot, Arnaud, “On the Origins of Comparative Advantage,”Journal of International Economics, April2009,77 (2), 255–64.

, Dave Donaldson, and Ivana Komunjer, “What Goods Do Countries Trade? A Quantitative Explo-ration of Ricardo’s Ideas,”Review of Economic Studies, April 2012,79 (2), 581–608.

Crooks, Gavin E., “The Amoroso Distribution,”ArXiv, May 2010,1005(3274), 1–27.

Cuñat, Alejandro and Marc J. Melitz, “Volatility, Labor Market Flexibility, and the Pattern of Compara-tive Advantage,”Journal of the European Economic Association, April 2012,10 (2), 225–54.

Davis, Donald R. and David E. Weinstein, “An Account of Global Factor Trade,”American EconomicReview, December 2001,91 (5), 1423–53.

Deardorff, Alan V., “Determinants of Bilateral Trade: Does Gravity Work in a Neoclassical World?,” inJeffrey A. Frankel, ed.,The Regionalization of the World Economy, Chicago: University of Chicago Press,January 1998, chapter 1, pp. 7–32.

Dennis, Brian, “Stochastic Differential Equations As Insect Population Models,” in Lyman L. McDonald,Bryan F. J. Manly, Jeffrey A. Lockwood, and Jesse A. Logan, eds.,Estimation and Analysis of InsectPopulations, Vol. 55 ofLecture Notes in Statistics, New York: Springer, 1989, chapter 4, pp. 219–238.Proceedings of a Conference held in Laramie, Wyoming, January 25-29, 1988.

Easterly, William and Ariell Reshef, “African Export Successes: Surprises, Stylized Facts, and Explana-tions,” NBER Working Paper, 2010,16597.

Eaton, Jonathan and Samuel Kortum, “International Technology Diffusion: Theory and Measurement,”International Economic Review, August 1999,40 (3), 537–70.

and , “Technology, Geography, and Trade,”Econometrica, September 2002,70 (5), 1741–79.

and , “Technology in the Global Economy: A Framework for Quantitative Analysis,” March 2010.University of Chicago, unpublished manuscript.

, Samuel S. Kortum, and Sebastian Sotelo, “International Trade: Linking Micro and Macro,”NBERWorking Paper, 2012,17864.

Fadinger, Harald and Pablo Fleiss, “Trade and Sectoral Productivity,”Economic Journal, September 2011,121(555), 958–89.

Fally, Thibault, “Structural Gravity and Fixed Effects,” July 2012. University of California, Berkeley,unpublished manuscript.

Feenstra, Robert C., Robert E. Lipsey, Haiyan Deng, Alyson C. Ma, and Hengyong Mo, “World TradeFlows: 1962-2000,”NBER Working Paper, January 2005,11040.

Finicelli, Andrea, Patrizio Pagano, and Massimo Sbracia, “Trade-Revealed TFP,”Bank of Italy Temi diDiscussione (Working Paper), October 2009,729.

, , and , “Ricardian Selection,”Journal of International Economics, January 2013,89 (1), 96–109.

61

Forman, Julie L. and Michael Sørensen, “The Pearson Diffusions: A Class of Statistically TractableDiffusion Processes,”Scandinavian Journal of Statistics, September 2008,35 (3), 438–465.

and , “A Transformation Approach to Modelling Multi-modal Diffusions,”Journal of Statistical Plan-ning and Inference, 2013, p. forthcoming (available online 7 October 2013).

Freund, Caroline L. and Martha D. Pierola, “Export Superstars,” September 2013. The World Bank,unpublished manuscript.

Grossman, Gene M. and Elhanan Helpman, “Quality Ladders in the Theory of Growth,”Review of Eco-nomic Studies, January 1991,58 (1), 43–61.

Hansen, Lars P., “Large Sample Properties of Generalized Method of Moments Estimators,”Econometrica,July 1982,50 (4), 1029–54.

Hanson, Gordon H., “The Rise of Middle Kingdoms: Emerging Economies in Global Trade,”Journal ofEconomic Perspectives, Spring 2012,26 (2), 41–64.

Hausmann, Ricardo, Jason Hwang, and Dani Rodrik, “What You Export Matters,”Journal of EconomicGrowth, March 2007,12 (1), 1–25.

Helpman, Elhanan, Marc Melitz, and Yona Rubinstein, “Estimating Trade Flows: Trading Partners andTrading Volumes,”Quarterly Journal of Economics, May 2008,123(2), 441–87.

Imbs, Jean and Romain Wacziarg, “Stages of Diversification,”American Economic Review, March 2003,93 (1), 63–86.

Karlin, Samuel and Howard M. Taylor, A second course in stochastic processes, 1st ed., New York:Academic Press, 1981.

Kerr, William R., “Heterogeneous Technology Diffusion and Ricardian Trade Patterns,”NBER WorkingPaper, November 2013,19657.

Kessler, Mathieu and Michael Sørensen, “Estimating Equations Based on Eigenfunctions for a DiscretelyObserved Diffusion Process,”Bernoulli, April 1999,5 (2), 299–314.

Kotz, Samuel, Norman L. Johnson, and N. Balakrishnan,Continuous Univariate Distributions, 2nd ed.,Vol. 1 of Wiley Series in Probability and Statistics, New York: Wiley, October 1994.

Krugman, Paul R., “Scale Economies, Product Differentiation, and the Pattern of Trade,”American Eco-nomic Review, December 1980,70 (5), 950–59.

Leigh, Egbert G., “The Ecological Role of Volterra’s Equations,” in Murray Gerstenhaber, ed.,Some math-ematical problems in biology, Vol. 1 ofLectures on mathematics in the life sciences, Providence, RhodeIsland: American Mathematical Society, December 1968, pp. 19–61. Proceedings of the Symposium onMathematical Biology held at Washington, D.C., December 1966.

Levchenko, Andrei A., “Institutional Quality and International Trade,”Review of Economic Studies, July2007,74 (3), 791–819.

and Jing Zhang, “The Evolution of Comparative Advantage: Measurement and Welfare Implications,”January 2013. University of Michigan, unpublished manuscript.

62

Lunde, Asger and Anne F. Brix, “Estimating Stochastic Volatility Models using Prediction-based Estimat-ing Functions,”CREATES Research Paper, July 2013,23.

Luttmer, Erzo G. J., “Selection, Growth, and the Size Distribution of Firms,”Quarterly Journal of Eco-nomics, August 2007,122(3), 1103–44.

Melitz, Marc J., “The Impact of Trade on Intra-Industry Reallocations and Aggregate Industry Productiv-ity,” Econometrica, November 2003,71 (6), 1695–1725.

Pearson, Karl, “Contributions to the Mathematical Theory of Evolution. II. Skew Variation in Homoge-neous Material,”Philosophical Transactions of the Royal Society of London. A, November 1895,186,343–414.

Prajneshu, “Time-Dependent Solution of the Logistic Model for Population Growth in Random Environ-ment,”Journal of Applied Probability, December 1980,17 (4), 1083–1086.

Quah, Danny T., “Convergence Empirics across Economies with (Some) Capital Mobility,”Journal ofEconomic Growth, March 1996,1 (1), 95–124.

Romalis, John, “Factor Proportions and the Structure of Commodity Trade,”American Economic Review,March 2004,94 (1), 67–97.

Schott, Peter K., “One Size Fits All? Heckscher-Ohlin Specialization in Global Production,”AmericanEconomic Review, June 2003,93 (3), 686–708.

Shikher, Serge, “Capital, Technology, and Specialization in the Neoclassical Model,”Journal of Interna-tional Economics, March 2011,83 (2), 229–42.

, “Putting Industries into the Eaton-Kortum Model,”Journal of International Trade and Economic Devel-opment, December 2012,21 (6), 807–37.

Silva, João M. C. Santos and Silvana Tenreyro, “The Log of Gravity,”Review of Economics and Statistics,November 2006,88 (4), 641–58.

Sørensen, Michael, “Statistical Inference for Integrated Diffusion Processes,” in International StatisticalInstitute, ed.,Proceedings of the 58th World Statistics Congress 2011, Dublin 2011, pp. 75–82.

Stacy, E. W., “A Generalization of the Gamma Distribution,”Annals of Mathematical Statistics, September1962,33 (3), 1187–1192.

Sutton, John, “Gibrat’s Legacy,”Journal of Economic Literature, March 1997,35 (1), 40–59.

Trefler, Daniel, “The Case of the Missing Trade and Other Mysteries,”American Economic Review, De-cember 1995,85 (5), 1029–46.

Vasicek, Oldrich A., “An Equilibrium Characterization of the Term Structure,”Journal of Financial Eco-nomics, November 1977,5 (2), 177–88.

Waugh, Michael E., “International Trade and Income Differences,”American Economic Review, December2010,100(5), 2093–2124.

Wong, Eugene, “The Construction of a Class of Stationary Markoff Processes,” in Richard Bellman, ed.,Stochastic processes in mathematical physics and engineering, Vol. 16 ofProceedings of symposia inapplied mathematics, Providence, R.I.: American Mathematical Society, 1964, chapter 12, pp. 264–276.

63